$course$/top/CSSBE $course$/top/CSSBE/Sec 4 $course$/top/CSSBE/Sec 4/Algèbre Test mise en forme 1.0000000 0.0000000 0 daniel__RECIT__SN4__Fractions_rationnelles__Addition_1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes/1.1.1 - Nombre de termes et degré d'un polynôme OP_POLY Algèbre_vocabulaire_degré Donne le degré de chaque expression algébrique.


Expression     
 Degré
#p11 {#1}
#p21 {#2}
#p31 {#3}
#p41 {#4}



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]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi><mo>,</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>L</mi><mo>.</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p11</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p31</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p41</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>,</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Algèbre_vocabulaire-1 Complète le tableau en choisissant le nom associé à chaque expression algébrique.


Expression      
Nom
#p1 {#1}
#p2 {#2}
#p3 {#3}
#p4 {#4}


]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad11</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad21</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad12</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad22</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad13</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad23</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad14</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad24</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms><mo>,</mo><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>trinôme</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Algèbre_vocabulaire-2 Complète le tableau en choisissant le nom associé à chaque expression algébrique.


Expression      
Nom
#p1 {#1}
#p2 {#2}
#p3 {#3}
#p4 {#4}


]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad11</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad21</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad12</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad22</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad13</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad23</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad14</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad24</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms><mo>,</mo><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>trinôme</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation FAC Consignes[ID:consigne_facto] Pour factoriser les trinômes qui vont suivre, tu peux t'inspirer de l'exemple ci-dessous.


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0.0000000 0.0000000 0 $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes/1.1.5 - Mise en évidence simple FactoSimpDoub1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP31__Facto1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course alg_ME-1 Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fac</mi><mo>=</mo><mi>gcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> alg_ME-2_fonctionnel Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>a</mi><mi>e</mi></msup><mo>+</mo><mi>c</mi><mo>*</mo><msup><mi>a</mi><mrow><mi>e</mi><mo>-</mo><mn>2</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>x</mi><mo>=</mo><mi>p</mi><mo>)</mo><mo>∧</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>a</mi><mrow><mi>e</mi><mo>-</mo><mn>2</mn></mrow></msup></mrow><mrow><mi>credit</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>(</mo><mi>x</mi><mo>=</mo><mi>p</mi><mo>)</mo><mo>∧</mo><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>≠</mo><mi>b</mi><mo>*</mo><msup><mi>a</mi><mi>e</mi></msup></mrow></mfenced></mrow><mrow><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">true</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> alg_ME-3 Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>f</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>g</mi></mtd></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mrow><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>c1</mi></mrow></mfenced><mo>&gt;</mo><msup><mi>b1</mi><mn>2</mn></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>2</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>,</mo><integers/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfenced><mrow><mfrac><msqrt><mn>13</mn></msqrt><mn>2</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mfrac><msqrt><mn>13</mn></msqrt><mn>2</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 06 : réduire fraction algébrique par MES - réponse fraction Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>n</mi><mi>m</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation/1.2.1 - Double mise en évidence FAC_DME Facto_Double_1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP31__Facto2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP31__Facto3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_4 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_5 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto4.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_6 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto5.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_7 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto6.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_Double_8 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto7.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course FactoSimpDoub2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP31__Facto2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course FactoSimpDoub3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP31__Facto3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course DME-1_(ax+b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 DME_MEPQ1 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-2(ax-b)(cx-d) Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

Débutons par une première mise en évidence sur chaque paire de termes:

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1, on obtient:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»*«/mo»«mi»x«/mi»«mo»*«/mo»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«mo»)«/mo»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol


]]> 1.0000000 0.3333333 0 DME_MEPQ2 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-2(coeff neg) Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1, on obtient:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»*«/mo»«mi»x«/mi»«mo»*«/mo»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«mo»)«/mo»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol






]]> 1.0000000 0.3333333 0 DME_MEPQ3 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation/1.2.4 - Trinôme carré parfait Facto_TrinomeCarreParfait_1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_TrinomeCarreParfait_2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_TrinomeCarreParfait_3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto15.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_TrinomeCarreParfait_4 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto17.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course TriCarrPar2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_CP-1 Factorise le polynôme suivant:

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_CP-2 Factorise le polynôme suivant:

#p1

]]>

Nous avons ici un trinôme carré parfait.

En effet,

#c1 est le carré de #c3

#c2 correspond au carré de #b

et #dp est le double produit de #c3 par #b.

La factorisation est donc: #sol


]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mo>(</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dp</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>140</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation/1.2.2 - Différence de carrés DiffCarr1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course DiffCarr2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course DiffCarr3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DifférenceCarre_1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DifferenceCarre_2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DifferenceCarre_3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP32__DiffCarr3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DifferenceCarre_4 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto11.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DifferenceCarre_5 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto13.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_DC-1 Factorise la différence de carrés suivante:

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto-DC-2(Jordi) Factorise le polynôme suivant:

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">true</property><property name="item_separator">,</property><property name="lang">en</property><property name="precision">4</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>until</mi><mo>&#xA0;</mo><mi>gcd</mi><mfenced><mrow><mi mathvariant="normal">a</mi><mo>,</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mo>==</mo><mn>1</mn><mo>&#x2227;</mo><mfenced><mrow><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>&#x2209;</mo><mi mathvariant="normal">&#x2115;</mi><mo>&#x2228;</mo><msqrt><mi mathvariant="normal">b</mi></msqrt><mo>&#x2209;</mo><mi mathvariant="normal">&#x2115;</mi></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>string_substitution</mi><mfenced><mrow><mo>&quot;</mo><mfenced><mrow><mo>#</mo><mn>1</mn></mrow></mfenced><mo>&#xB7;</mo><mfenced><mrow><mo>#</mo><mn>2</mn></mrow></mfenced><mo>&quot;</mo><mo>,</mo><mi>p1</mi><mo>,</mo><mi>p2</mi></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>"</mo><mfenced><mrow><mn>7</mn><mo>·</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced><mo>·</mo><mfenced><mrow><mn>7</mn><mo>·</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn></mrow></mfenced><mo>"</mo></mrow></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">u</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#x2227;</mo><msub><mi mathvariant="normal">u</mi><mn>1</mn></msub><mo>&#x2260;</mo><mi>coefficient</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn><mi mathvariant="normal">e</mi></mrow></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mrow><mn>2</mn><mi mathvariant="normal">e</mi></mrow></msup><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">true</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation/1.2.3 - Trinôme x^2+bx+c (somme-produit) Facto_SommeProduit_1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_SommeProduit_2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf4.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_SommeProduit_3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto19.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_SommeProduit_4 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto21.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_SommeProduit_degre4_1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV3__Facto22.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course TriCarrPar1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course TriCarrPar3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course TriCarrPar4 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP33__TriCarrParf4.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Facto_x^2+bx+x_1[ID:facto_1] Factorise le polynôme ci-dessous.

#p1

]]> On a ici un polynôme de la forme: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math».

Il faut trouver deux nombres dont le produit est #p et dont la somme égale #s1 . Ces deux nombres sont: #a et #b.

La factorisation de #p1 est donc #sol.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mi>a</mi><mo>≠</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Factorisation-1 (somme-produits) Factorise le polynôme suivant:

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mo> </mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mo> </mo><mi>a2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>prod1</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>0</mn><mo>*</mo><mi>p1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>som1</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>38</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>prod1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>som1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.2 - Factorisation/1.2.5 - Trinôme ax^2+bx+c Trinôme ax^2+bx+c Factorise le trinôme suivant:

#p2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m2</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m2</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>m1</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m1</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>m2</mi><mo>.</mo><mn>1</mn></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille de calculs</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Trinôme ax^2+bx+c (2) Factorise le trinôme suivant:

#p2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m2</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m2</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>m1</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m1</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>m2</mi><mo>.</mo><mn>1</mn></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille de calculs</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.4 - Opérations sur les fractions rationnelles $course$/top/CSSBE/Sec 4/Algèbre/1.4 - Opérations sur les fractions rationnelles/1.4.2 - Addition et soustraction d'expressions rationnelles Addition_simple Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple_Restrictions Effectue l'addition demandée.  Ne pas oublié la ou les restrictions.(exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse=#solRestrictions= #restric]]> Réponse=#solRestrictions=#restric2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mo>-</mo><mi>d</mi><mo>/</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mi>d</mi><mo>/</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mfenced><mi>s</mi></mfenced><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mfenced><mi>s</mi></mfenced><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \s</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30 70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_avec restrictions Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» tu peux seulement écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> Réponse simplifiée=#solRestrictions=#restr2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L2</mi><mo>,</mo><mi>x</mi><mo>≠</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr2</mi><mo>=</mo><mi>L2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>19</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>106</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>≠</mo><mo>-</mo><mn>5</mn><mo>,</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_simple Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_common_denominator"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.4 - Opérations sur les fractions rationnelles/1.4.3 - Multiplication d'expressions rationnelles Multiplication_simple Effectue la multiplication demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.4 - Opérations sur les fractions rationnelles/1.4.4 - Division d'expressions rationnelles Division_simple Effectue la division demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></mrow><mrow><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>43</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.3 - Division de polynômes DivPoly1 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP22__DivPoly1.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course DivPoly2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP22__DivPoly2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Division_forme-1_avec_reste_possible Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 -#pr1    #d1+#d2#s2#dd3  Pour déterminer #d1 nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
-#pr2      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer #d2 nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mi>f</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>76</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>47</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn><mo>,</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Division_forme-1_sans reste Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>11</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>21</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>7</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Division_forme-3_avec reste possible Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math 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close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/Test-diagnostique: Manipulations algébriques Décimaux_division_naturel-1**** (copie) Effectue les divisions suivantes.

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»§#247;«/mo»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/math»  {#1}

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mo»§#247;«/mo»«mo»#«/mo»«mi»n«/mi»«mn»4«/mn»«/math»  {#2}

c) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«mo»§#247;«/mo»«mo»#«/mo»«mi»n«/mi»«mn»6«/mn»«/math»  {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mi>list</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>random</mi><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>L1</mi><mn>3</mn></apply><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>L</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>L</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>L</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>max1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>max1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>max1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>n4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>n5</mi><mo>*</mo><mi>n6</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9.7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38.8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2.2</mn><mo>,</mo><mn>3.5</mn><mo>,</mo><mn>9.7</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1.1</mn><mo>,</mo><mn>1.2</mn><mo>,</mo><mn>1.3</mn><mo>,</mo><mn>1.4</mn><mo>,</mo><mn>1.5</mn><mo>,</mo><mn>1.6</mn><mo>,</mo><mn>1.7</mn><mo>,</mo><mn>1.8</mn><mo>,</mo><mn>1.9</mn><mo>,</mo><mn>2.1</mn><mo>,</mo><mn>2.2</mn><mo>,</mo><mn>2.3</mn><mo>,</mo><mn>2.4</mn><mo>,</mo><mn>2.5</mn><mo>,</mo><mn>2.6</mn><mo>,</mo><mn>2.7</mn><mo>,</mo><mn>2.8</mn><mo>,</mo><mn>2.9</mn><mo>,</mo><mn>3.1</mn><mo>,</mo><mn>3.2</mn><mo>,</mo><mn>3.3</mn><mo>,</mo><mn>3.4</mn><mo>,</mo><mn>3.5</mn><mo>,</mo><mn>3.6</mn><mo>,</mo><mn>3.7</mn><mo>,</mo><mn>3.8</mn><mo>,</mo><mn>3.9</mn><mo>,</mo><mn>4.1</mn><mo>,</mo><mn>4.2</mn><mo>,</mo><mn>4.3</mn><mo>,</mo><mn>4.4</mn><mo>,</mo><mn>4.5</mn><mo>,</mo><mn>4.6</mn><mo>,</mo><mn>4.7</mn><mo>,</mo><mn>4.8</mn><mo>,</mo><mn>4.9</mn><mo>,</mo><mn>5.1</mn><mo>,</mo><mn>5.2</mn><mo>,</mo><mn>5.3</mn><mo>,</mo><mn>5.4</mn><mo>,</mo><mn>5.5</mn><mo>,</mo><mn>5.6</mn><mo>,</mo><mn>5.7</mn><mo>,</mo><mn>5.8</mn><mo>,</mo><mn>5.9</mn><mo>,</mo><mn>6.1</mn><mo>,</mo><mn>6.2</mn><mo>,</mo><mn>6.3</mn><mo>,</mo><mn>6.4</mn><mo>,</mo><mn>6.5</mn><mo>,</mo><mn>6.6</mn><mo>,</mo><mn>6.7</mn><mo>,</mo><mn>6.8</mn><mo>,</mo><mn>6.9</mn><mo>,</mo><mn>7.1</mn><mo>,</mo><mn>7.2</mn><mo>,</mo><mn>7.3</mn><mo>,</mo><mn>7.4</mn><mo>,</mo><mn>7.5</mn><mo>,</mo><mn>7.6</mn><mo>,</mo><mn>7.7</mn><mo>,</mo><mn>7.8</mn><mo>,</mo><mn>7.9</mn><mo>,</mo><mn>8.1</mn><mo>,</mo><mn>8.2</mn><mo>,</mo><mn>8.3</mn><mo>,</mo><mn>8.4</mn><mo>,</mo><mn>8.5</mn><mo>,</mo><mn>8.6</mn><mo>,</mo><mn>8.7</mn><mo>,</mo><mn>8.8</mn><mo>,</mo><mn>8.9</mn><mo>,</mo><mn>9.1</mn><mo>,</mo><mn>9.2</mn><mo>,</mo><mn>9.3</mn><mo>,</mo><mn>9.4</mn><mo>,</mo><mn>9.5</mn><mo>,</mo><mn>9.6</mn><mo>,</mo><mn>9.7</mn><mo>,</mo><mn>9.8</mn><mo>,</mo><mn>9.9</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="casSession"/></localData></question> Isole la variable « y » dans cette équation :

#e1 = 0

Réponse : y = {#1}

]]> #e1 = 0    --> Envoyer les termes qui ne sont pas des "y" à droite du "=".        

#f y = #c x  +  #d    --> Diviser tous les termes par #f, dans le but d'avoir 1 seul "y" à gauche du "=" (isoler "y").

y = #a x  +  #b

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>63</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Isole la variable « y » dans cette équation :

#e2 = #e1

Réponse : y = {#1}

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/math»        --> Envoyer le terme en "y" à gauche du "=",  et les autres à droite du "=".

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»    --> Diviser tous les termes par #f, dans le but d'avoir 1 seul "y" à gauche du "=" (isoler "y").

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«/math»

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>25</mn><mo>.</mo><mo>.</mo><mn>25</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mo>-</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>-</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Nombres_divisibilité-1(2-3-4-5-10) Indique si le nombre suivant est divisible par les nombres données.

#n

 

Divisible par : 2 3 4 5 10
Oui ou non {#1} {#2} {#3} {#4} {#5}

]]> 5.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MIN</mi><mo>=</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MAX</mi><mo>=</mo><mn>150</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mi>MIN</mi><mo>.</mo><mo>.</mo><mi>MAX</mi><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>L</mi><mo>.</mo><mi>i</mi><mo>==</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>L2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L2</mi><mo>,</mo><mi>oui</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L1</mi><mo>,</mo><mi>non</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>L2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L2</mi><mo>,</mo><mi>non</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L1</mi><mo>,</mo><mi>oui</mi><mo>)</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol6</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol7</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>7</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol8</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad4</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad5</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad6</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad7</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>7</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad8</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mn>8</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>non</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>oui</mi></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>oui</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>oui</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>non</mi><mo>,</mo><mi>non</mi></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="casSession"></data></localData></question> Q10 - Quotient d'une même puissance d'entier Représente les expressions données sous la forme d'une base fractionnaire ou entière affectée d'un seul exposant. Pour ce faire, clique sur le symbole et utilise les outils proposés en respectant les conventions d'écriture mathématique.



A)
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«msup»«mi»e«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»c«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«mo»=«/mo»«/math»   

{#1}


B)
  
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«msup»«mi»j«/mi»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»h«/mi»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«mo»=«/mo»«/math»
{#2}

C)
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«msup»«mi»o«/mi»«mrow»«mo»#«/mo»«mi»l«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»m«/mi»«mrow»«mo»#«/mo»«mi»l«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math» =
{#3}

D)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«msup»«mi»t«/mi»«mrow»«mo»#«/mo»«mi»q«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»r«/mi»«mrow»«mo»#«/mo»«mi»q«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«/math»
{#4}

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>,</mo><mi>a</mi><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mfenced><mfrac><mi>e</mi><mi>c</mi></mfrac></mfenced><mi>b</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>256</mn><mn>2401</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>,</mo><mi>f</mi><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn></math></output></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><msup><mfenced><mfrac><mi>o</mi><mi>m</mi></mfrac></mfenced><mi>l</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>64</mn><mn>25</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>4</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>14</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>,</mo><mi>p</mi><mo>}</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><msup><mfenced><mfrac><mi>t</mi><mi>r</mi></mfrac></mfenced><mi>q</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>64</mn><mn>25</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_simplified"/><assertion name="check_minimal_radicands"/><assertion name="check_no_common_factor"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/><assertion name="check_fraction_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Test diag - Notions de base Q11 - Simplification de radicaux Pour chacune des expressions données, identifie la bonne expression simplifiée.


  1.   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«mi»c«/mi»«/msqrt»«/math» 
  {#1}
]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msqrt><mi>b</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>*</mo><msqrt><mi>b</mi></msqrt><mo>*</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mfrac><msqrt><mi>c</mi></msqrt><mi>a</mi></mfrac><mo>*</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt><mo>*</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Test diag - Notions de base Q12 - Simplification de radicaux Quelle est la forme  simplifiée du radical ci-dessous?


  1.   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mo»#«/mo»«mi»c«/mi»«/msqrt»«/math»    {#1}
]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msqrt><mi>b</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>*</mo><msqrt><mi>b</mi></msqrt><mo>*</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mfrac><msqrt><mi>c</mi></msqrt><mi>a</mi></mfrac><mo>*</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt><mo>*</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="check_minimal_radicands"/><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Test diag - Notions de base Isole la variable « y » dans cette équation :

#e1 = 0

Réponse : y = {#1}

]]> #e1 = 0    --> Envoyer les termes qui ne sont pas des "y" à droite du "=".        

#f y = #c x  +  #d    --> Diviser tous les termes par #f, dans le but d'avoir 1 seul "y" à gauche du "=" (isoler "y").

y = #a x  +  #b

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>63</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Isole la variable « y » dans cette équation :

#e2 = #e1

Réponse : y = {#1}

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/math»        --> Envoyer le terme en "y" à gauche du "=",  et les autres à droite du "=".

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»    --> Diviser tous les termes par #f, dans le but d'avoir 1 seul "y" à gauche du "=" (isoler "y").

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«/math»

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>25</mn><mo>.</mo><mo>.</mo><mn>25</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mo>-</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>-</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Soit l'équation suivante : #e1 = 0 .

a) Si « x » vaut #n1   , alors « y » vaudra {#1} .

b) Si "y" vaut #n1   , alors « x » vaudra {#2} .

Note 1 : Si une réponse n'est pas un entier, écris cette réponse en fraction (ex. : -1/3 et non -0,3333).

]]> a) 

  • On isole « y » :

y = #e

  • Puis on remplace « x » par #n1, et on calcule la valeur de "y" :

y = #a * #n1 + #b

y = #r1

b) 

  • On isole « y » :

y = #e

  • Puis on remplace « y » par #n1, et on calcule la valeur de « x » :

#n1 = #e

#n1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«/math» #b = #a x

#c = #a x

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfrac»«/math» = x

#r2 = x

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>/</mo><mo>[</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>[</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>n1</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n1</mi><mo>-</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">false</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="tolerance_digits">2</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q4 - Fractions_pourcentage_tableau Le tableau ci-dessous donne les résultats de 4 de tes amis lors du dernier examen de géographie.  Complète la dernière colonne de ce tableau.

Prénom

Note sur

#NOTE

Note sur

100
#nom1 #n1 {#1}
#nom2 #n2 {#2}
#nom3 #n3 {#3}
#nom4 #n4 {#4}

 

 

 

 

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align="center"><mtr><mtd><mn>27</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>15</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="casSession"></data></localData></question> Test diag - Notions de base Q5 - Fractions_réduire Réduis chaque fraction à sa plus simple expression.

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»       {#1}

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»       {#2}

c) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»5«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfrac»«/math»       {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n11</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n12</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n13</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>11</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>n11</mi><mo>≠</mo><mi>n12</mi><mo>∧</mo><mi>n11</mi><mo>≠</mo><mi>n13</mi><mo>∧</mo><mi>n12</mi><mo>≠</mo><mi>n13</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>n1</mi><mo>/</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>n12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>n3</mi><mo>/</mo><mi>n4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n5</mi><mo>=</mo><mi>n13</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n6</mi><mo>=</mo><mi>n5</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>n5</mi><mo>/</mo><mi>n6</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="casSession"></data></localData></question> Test diag - Notions de base Q6 - Fraction_x_naturel Effectue les multiplications suivantes.  Réduire le résultat à sa plus simple expression.

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«mo»§#215;«/mo»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/math» {#1}

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«mo»§#215;«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«/math» {#2}

c) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»3«/mn»«mo»§#215;«/mo»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«/math» {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>list</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mi>random</mi><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>L</mi><mn>3</mn></apply><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>/</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>/</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>/</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><naturalnumbers/><mo>∧</mo><mi>f2</mi><mo>∉</mo><naturalnumbers/><mo>∧</mo><mi>f3</mi><mo>∉</mo><naturalnumbers/><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f2</mi><mo>∧</mo><mi>f2</mi><mo>≠</mo><mi>f3</mi><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f3</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><msub><mi>L1</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><msub><mi>L1</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><msub><mi>L1</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>f1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>f2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>f3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="casSession"></data></localData></question> Test diag - Notions de base Addition_monômes_xy-3[ID:add_mon] Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #de.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>e1</mi><mo>+</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_monômes-1 Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_monômes-1[ID:testP1] Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_monômes-2 Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte.  #sol

]]>  #bad1

]]>  #bad2

]]>  #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_monômes-2 Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Mod_1_proportion Sachant que le diviseur est #d1 et le dividende est #d2, quelle est la valeur du quotient?

]]> Puisque nous connaissons le dividende et le diviseur, il suffit de faire

Dividende «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#247;«/mo»«/math»Diviseur pour obtenir le quotient

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#247;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»                                                                                                

  division

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 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>d1</mi><mo>/</mo><mi>d2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.76</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44.032</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.23256</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">2</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option><option name="float_format">f</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Mod_1_proportion Sachant que le diviseur est #d1 et le dividende est #d2, quelle est la valeur du quotient?

]]> Puisque nous connaissons le dividende et le diviseur, il suffit de faire

Dividende «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#247;«/mo»«/math»Diviseur pour obtenir le quotient

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#247;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»                                                                                                

  division

]]> 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 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>d1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>d1</mi><mo>/</mo><mi>d2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.76</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44.032</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.23256</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">2</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option><option name="float_format">f</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q17 - Addition_monômes Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q18 - Addition_monômes Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes semblables de degré #e1.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q19 - Addition_monômes_xy Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #de.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>e1</mi><mo>+</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q20 - Soustraction_monômes_xy Quelle expression correspond à la somme ci-dessous?

#p1 - #p2

]]>

En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #de.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>e1</mi><mo>+</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q22 - Division_monômes Quelle expression algébrique simplifiée est équivalente à l'expression suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Question 05 : division des exposants Quelle expression algébrique simplifiée est équivalente à l'expression suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 05 : division des exposants 3ième_BIENFORMATÉ Quelle expression algébrique simplifiée est équivalente à l'expression suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«/msup»«mrow»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>o</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_monômes-1 (1.1.2) Quelle expression correspond à la différence ci-dessous?

#p1 - #p2

]]> En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Algèbre réduire Réduis l'expression suivante :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»=«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>)</mo><mo>*</mo><msup><mi>p</mi><mn>2</mn></msup><mo>-</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>)</mo><mo>*</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_expanded"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Algèbre réduire (copie) Réduis l'expression suivante :
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»p«/mi»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»=«/mo»«/math»]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>)</mo><mo>*</mo><msup><mi>p</mi><mn>2</mn></msup><mo>-</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>)</mo><mo>*</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_expanded"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> équation Trouve la valeur de x pour que l'égalité soit vraie.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«mi»u«/mi»«mi»l«/mi»«mi»t«/mi»«mi»i«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>multiple</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>g</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>-</mo><mi>d</mi><mo>*</mo><mo>(</mo><mi>e</mi><mo>*</mo><mi>g</mi><mo>+</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>g</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>multiple</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>441</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> exposant fraction Simplifie l'expression suivante.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><msup><mi>y</mi><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow></msup></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fraction rationnelle_9 Réduire la fraction suivante

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»*«/mo»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»*«/mo»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>b</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fraction_6 Additionne les fractions suivantes.  Simplie le plus possible.

#f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><naturalnumbers/><mo>∧</mo><mi>f2</mi><mo>∉</mo><naturalnumbers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>9</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>89</mn><mn>36</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> fraction_8 Effectue le calcul ci-dessous. Donne la réponse sous forme de fraction réduite.

#f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mrow style="color:#ffc800"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow/><maction actiontype="argument"><mtext>condition</mtext></maction></apply><mtext xml:lang="en">variables</mtext></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fraction_droite_numérique-3 (copie) Sur la droite numérique ci-dessous,  quelle fraction est indiquée par la flèche rouge?

 

 

 

#plotter1

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrer</mi><mo> </mo><mi>fenêtre</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>150</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>600</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Traçage</mi><mo> </mo><mi>des</mi><mo> </mo><mi>graduations</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>axe</mi><mo> </mo><mi>numérique</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>k1</mi><mo> </mo><mi>in</mi><mo> </mo><mi>j</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo><mo>)</mo></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Choix</mi><mo> </mo><mi>du</mi><mo> </mo><mi>premier</mi><mo> </mo><mi>nombre</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variable</mi><mo> </mo><mi>qui</mi><mo> </mo><mi>positionnera</mi><mo> </mo><mi>les</mi><mo> </mo><mn>2</mn><mo> </mo><mi>nombres</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>l</mi><mo>&apos;</mo><mi>axe</mi><mo> </mo><mi>numérique</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Choix</mi><mo> </mo><mi>du</mi><mo> </mo><mn>2</mn><mi>e</mi><mo> </mo><mi>nombre</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mn>1</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Positionnement</mi><mo> </mo><mi>des</mi><mo> </mo><mn>2</mn><mo> </mo><mi>nombres</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>t1</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>31</mn><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>31</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t1</mi><mo>,</mo><mi>t2</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variable</mi><mo> </mo><mi>k</mi><mo> </mo><mi>qui</mi><mo> </mo><mi>donne</mi><mo> </mo><mi>les</mi><mo> </mo><mi>positions</mi><mo> </mo><mi>disponibles</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>le</mi><mo> </mo><mi>segment</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>30</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Fenêtre</mi><mo> </mo><mi>de</mi><mo> </mo><mi>sortie</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>visible</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Choix</mi><mo> </mo><mi>des</mi><mo> </mo><mi>attributs</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi><mo>,</mo><mi>fill</mi><mo>=</mo><mi>true</mi><mo>,</mo><mi>fill_colour</mi><mo>=</mo><mi>white</mi><mo>,</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi><mo>,</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi><mo>,</mo><mi>show_label</mi><mo>=</mo><mi>false</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg3</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Planche</mi><mo> </mo><mi>de</mi><mo> </mo><mi>travail</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>100</mn><mo>,</mo><mn>60</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Présentation</mi><mo> </mo><mi>graphique</mi><mo> </mo><mi>de</mi><mo> </mo><mi>tous</mi><mo> </mo><mi>les</mi><mo> </mo><mi>éléments</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>L</mi><mo>,</mo><mi>L2</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>arg1</mi><mo>,</mo><mi>W</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mo>(</mo><mi>k</mi><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo><mo>,</mo><mi>arg2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>95</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>45</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Réponse</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>n1</mi><mo>+</mo><mo>(</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>30</mn><mo>)</mo><mo>/</mo><mn>5</mn><mo>)</mo><mo>/</mo><mi>i</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>12</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Fraction_personne5 Affectue le calcul demandé. Donne la réponse sous la forme d'une fraction réduite.

#f + #g

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mrow style="color:#ffc800"/><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply style="color:#ffc800"><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr></mtable><mrow><mi>f</mi><mo>∉</mo><integers/><mo>∧</mo><mi>g</mi><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>numérateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>dénominateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>quotient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fraction_personne9 Calcule et donne la réponse sous la forme d'une fraction réduite:

#f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>numérateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>dénominateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>quotient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>9</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fractions 1 #f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f2</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f2</mi></mrow></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>43</mn><mn>72</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>9</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>43</mn><mn>72</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fractions_addition Effectue le calcul demandé.  Donne ta réponse sous la forme d'une fraction réduite.


#f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol #sol #n #p/#q]]> #n #p/#q]]> <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f2</mi><mo>∉</mo><integers/><mo> </mo><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>numérateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>dénominateur</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>quotient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol</correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#xA0;</mo><mo>#</mo><mi>p</mi><mo>/</mo><mo>#</mo><mi>q</mi></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#xA0;</mo><mo>#</mo><mi>p</mi><mo>/</mo><mo>#</mo><mi>q</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="equivalent_literal" correctAnswer="2"><param name="usecase">false</param><param name="usespaces">false</param></assertion><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Nombre décimal_entre 2 n.décimaux-1 (copie) Donne un nombre décimal situé entre les deux nombres données.

#n1  .........  #n2

]]> 1.0000000 0.3333333 0 0 3 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>n1</mi><mo>&lt;</mo><mi>n2</mi></mrow></apply></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>x</mi><mo>&gt;</mo><mi>n1</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>x</mi><mo>&lt;</mo><mi>n2</mi><mo>)</mo></mrow><mrow><mi>credit1</mi><mo>=</mo><mn>1</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit1</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9.564</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10.064</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>3</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-5)</option><option name="relative_tolerance">true</option><option name="precision">3</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="float_format">f</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Nombre_décimal_numérique-3_2 décimaux (copie) Sur la droite numérique ci-dessous,  quel nombre décimal est indiqué par la flèche rouge?

 

 

 

#plotter1

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paramétrer</mi><mo> </mo><mi>fenêtre</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>150</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>600</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Choix</mi><mo> </mo><mi>de</mi><mo> </mo><mn>2</mn><mo> </mo><mi>nombres</mi><mo> </mo><mi>décimaux</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mn>1</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Nombre</mi><mo> </mo><mi>de</mi><mo> </mo><mi>graduations</mi><mo> </mo><mi>entre</mi><mo> </mo><mi>les</mi><mo> </mo><mn>2</mn><mo> </mo><mi>nombres</mi><mo> </mo><mi>décimaux</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>==</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>j</mi><mo>=</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>k1</mi><mo> </mo><mi>in</mi><mo> </mo><mi>j</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mo>(</mo><mo>-</mo><mn>25</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>*</mo><mi>i</mi><mo>)</mo><mo>)</mo><mo>.</mo><mo>.</mo><mn>5</mn><mo>*</mo><mi>i</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>35</mn><mo>,</mo><mo>-</mo><mn>35</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>*</mo><mi>i</mi></mrow></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>37</mn><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>37</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>*</mo><mi>i</mi><mo>)</mo><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t1</mi><mo>,</mo><mi>t2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>P1</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>35</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>P2</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>35</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>*</mo><mi>i</mi><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>P3</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mi>k</mi><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mo>(</mo><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>35</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>*</mo><mi>i</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>j</mi><mo>=</mo><mi>list</mi><mo>(</mo><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>k1</mi><mo> </mo><mi>in</mi><mo> </mo><mi>j</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>,</mo><mi>point</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mo>(</mo><mo>-</mo><mn>20</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo><mo>)</mo><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>35</mn><mo>,</mo><mo>-</mo><mn>35</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi></mrow></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>t1</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>37</mn><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>t2</mi><mo>=</mo><mi>text_box</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>37</mn><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo><mo>,</mo><mo>-</mo><mn>15</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t1</mi><mo>,</mo><mi>t2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>P1</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>35</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>P2</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>35</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>P3</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mi>k</mi><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mo>(</mo><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>35</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variable</mi><mo> </mo><mi>k</mi><mo> </mo><mi>qui</mi><mo> </mo><mi>donne</mi><mo> </mo><mi>les</mi><mo> </mo><mi>positions</mi><mo> </mo><mi>disponibles</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>le</mi><mo> </mo><mi>segment</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>45</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>30</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>i</mi></mrow></mfenced><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Fenêtre</mi><mo> </mo><mi>de</mi><mo> </mo><mi>sortie</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>visible</mi><mo>=</mo><mi>true</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Choix</mi><mo> </mo><mi>des</mi><mo> </mo><mi>attributs</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi><mo>,</mo><mi>fill</mi><mo>=</mo><mi>true</mi><mo>,</mo><mi>fill_colour</mi><mo>=</mo><mi>white</mi><mo>,</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi><mo>,</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>red</mi><mo>,</mo><mi>show_label</mi><mo>=</mo><mi>false</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg3</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Planche</mi><mo> </mo><mi>de</mi><mo> </mo><mi>travail</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>100</mn><mo>,</mo><mn>60</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Présentation</mi><mo> </mo><mi>graphique</mi><mo> </mo><mi>de</mi><mo> </mo><mi>tous</mi><mo> </mo><mi>les</mi><mo> </mo><mi>éléments</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>L</mi><mo>,</mo><mi>L2</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>arg1</mi><mo>,</mo><mi>W</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>P3</mi><mo>,</mo><mi>arg2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>P1</mi><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>10</mn></mrow></mfenced><mo>,</mo><mi>P2</mi><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>tr</mi><mo>,</mo><mfenced close="]" open="["><mrow><mn>95</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mo>(</mo><mo>-</mo><mn>45</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>arg3</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>réponse</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mo>(</mo><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>30</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>5</mn><mo>*</mo><mi>i</mi><mo>)</mo></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.85</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Pourcentage_1 Effectue le calcul suivant.

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>500</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>380</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Pourcentage_2 Simplifie l'expression suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>b</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>8</mn></msup></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_4 Effectue le calcul suivant

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>90</mn><mo>.</mo><mo>.</mo><mn>150</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>105.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_6 Effectue le calcul suivant :

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>5000</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1400</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1260.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_7 Effectue le calcul suivant :
#n % de #m

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>10000</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8500</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5950.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Pourcentage_8 Effectue le calcul suivant:

#n % de #m

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>5000</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1800</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>630.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_personne10 Effectue le calcul suivant :

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Pourcentage_personne3 Effectue le calcul suivant:

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>60</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>500</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>440</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>176.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_personne5 Effectue le calcul suivant:

#p de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>1000</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144.</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pourcentage_personne9 Calcule

#p % de #n

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>des</mi><mo> </mo><mi>variables</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>95</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>99</mn><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>5000</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>n</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>85</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3700</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3145.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Produit_entiers Effectue le calcul ci-dessous:

#n1 x #n2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mi>n2</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>n2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Q1 - Nombres_divisibilité Écris un nombre naturel qui  se divise par les nombres suivants: #L

 

]]> 1.0000000 0.3333333 0 0 1 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>random</mi><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>D</mi><mi>i</mi></apply><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>j</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>a</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x</mi><mo> </mo><mi>mod</mi><mo> </mo><mi>L</mi><mo>.</mo><mi>j</mi><mo>==</mo><mn>0</mn></mrow><mrow><mi>L1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L1</mi><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>L1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L1</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow></apply></apply></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>k</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>a</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>s</mi><mo>+</mo><mi>L1</mi><mo>.</mo><mi>k</mi></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mi>a</mi></mrow><mrow><mi>credit</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>credit</mi><mo>=</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Test diag - Notions de base Q16 - Dette_Julie Pour rembourser une dette, Julie effectue 4 versements. Le premier représente #v1 de la dette, le second, #v2 et le troisième, #v3. Le quatrième versement est de #v4 $. Quel est le montant de la dette ?

]]> 1.0000000 0.3333333 0 0 #sol #sol $]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Initialisation</mi><mo> </mo><mi>de</mi><mo> </mo><mn>2</mn><mo> </mo><mi>vecteurs</mi><mo> </mo><mi>avec</mi><mo> </mo><mi>les</mi><mo> </mo><mi>fractions</mi><mo> </mo><mi>usuelles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>moitié</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>tiers</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>quart</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>cinquième</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>sixième</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>huitième</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>la</mi><mo> </mo><mi>moitié</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>tiers</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>quart</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>cinquième</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>sixième</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>le</mi><mo> </mo><mi>huitième</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>8</mn></mfrac></mtd></mtr></mtable></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>le</mi><mo> </mo><mi>montant</mi><mo> </mo><mi>v4</mi><mo> </mo><mi>est</mi><mo> </mo><mi>celui</mi><mo> </mo><mi>en</mi><mo> </mo><mi>argent</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>80</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>je</mi><mo> </mo><mi>fais</mi><mo> </mo><mi>un</mi><mo> </mo><mi>random</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>quelle</mi><mo> </mo><mi>fraction</mi><mo> </mo><mi>commencée</mi><mo> </mo><mi>en</mi><mo> </mo><mi>omettant</mi><mo> </mo><mn>1</mn><mo>/</mo><mn>2</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>je</mi><mo> </mo><mi>détermine</mi><mo> </mo><mi>les</mi><mo> </mo><mn>3</mn><mo> </mo><mi>fractions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>L1</mi><mo>.</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>&apos;</mo><mi>additionne</mi><mo> </mo><mi>les</mi><mo> </mo><mn>3</mn><mo> </mo><mi>fractions</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tot</mi><mo>=</mo><mi>L2</mi><mo>.</mo><mi>a</mi><mo>+</mo><mi>L2</mi><mo>.</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>L2</mi><mo>.</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>solution</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>v4</mi><mo>/</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>tot</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>le</ms><mo> </mo><ms>huitième</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>la</ms><mo> </mo><ms>moitié</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>le</ms><mo> </mo><ms>tiers</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tot</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>23</mn><mn>24</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2160.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mo> </mo><mo>$</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_quantity"><param name="units">$, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="float_format">f</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> test diag - manipulations algébriques Q21 - Multiplication_monomes Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>56</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> test diag - manipulations algébriques Q3 - Pourcent_nombre Effectue le calcul suivant:

#p1% de #n1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>100</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>50</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>n1</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>190</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>152.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="float_format">f</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Test diag - Notions de base Q7 - Fractions_addition Effectue le calcul suivant

#f1 + #f2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></mtd></mtr></mtable><mrow><mi>f1</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f2</mi><mo>∉</mo><integers/><mo>∧</mo><mi>f1</mi><mo>≠</mo><mi>f2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>85</mn><mn>24</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Test diag - Notions de base Q8 - Fraction_soustraction Effectue la soustraction de ces fractions.  Réduire le résultat à sa plus simple expression.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol #sol #n #p/#q]]> #n #p/#q]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>i</mi><mo>*</mo><mi>d1</mi></mtd></mtr></mtable><mrow><mi>n1</mi><mo>&gt;</mo><mi>n2</mi><mo>∧</mo><mi>n1</mi><mo>/</mo><mi>d1</mi><mo>∉</mo><naturalnumbers/><mo>∧</mo><mi>n2</mi><mo>/</mo><mi>d2</mi><mo>∉</mo><naturalnumbers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n1</mi><mo>/</mo><mi>d1</mi><mo>-</mo><mi>n2</mi><mo>/</mo><mi>d2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>numerator</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>denominator</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>quotient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mrow><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>p</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>q</mi><mo>=</mo><mi>b</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>27</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol</correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo> </mo><mo>#</mo><mi>p</mi><mo>/</mo><mo>#</mo><mi>q</mi></math>]]></correctAnswer><correctAnswer id="3" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo> </mo><mo>#</mo><mi>p</mi><mo>/</mo><mo>#</mo><mi>q</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="equivalent_literal" correctAnswer="2"><param name="usecase">false</param><param name="usespaces">false</param></assertion><assertion name="equivalent_symbolic" correctAnswer="3"/><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Test diag - Notions de base Q9 - Fractions_soustraction Effectue l'opération suivante : #f1 #s1 #f3

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mn>1000</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pour</mi><mo> </mo><mi>ne</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>avoir</mi><mo> </mo><mi>un</mi><mo> </mo><mi>dénominateur</mi><mo> </mo><mi>trop</mi><mo> </mo><mi>gros</mi><mo> </mo><mo>(</mo><mo>&lt;</mo><mn>150</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>b1</mi><mo>&gt;</mo><mn>150</mn></mrow><mtable><mtr><mtd><mi>n11</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>;</mo><mi>n12</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>;</mo><mi>b11</mi><mo>=</mo><mi>aléa</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>;</mo><mi>b12</mi><mo>=</mo><mi>aléa</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><msup><mi>b11</mi><mi>n11</mi></msup><mo>*</mo><msup><mi>b12</mi><mi>n12</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>a1</mi><mi>b1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mn>1000</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pour</mi><mo> </mo><mi>ne</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>avoir</mi><mo> </mo><mi>un</mi><mo> </mo><mi>dénominateur</mi><mo> </mo><mi>trop</mi><mo> </mo><mi>gros</mi><mo> </mo><mo>(</mo><mo>&lt;</mo><mn>150</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>b2</mi><mo>&gt;</mo><mn>150</mn></mrow><mtable><mtr><mtd><mi>n21</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>;</mo><mi>n22</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>;</mo><mi>b21</mi><mo>=</mo><mi>aléa</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>;</mo><mi>b22</mi><mo>=</mo><mi>aléa</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><msup><mi>b21</mi><mi>n21</mi></msup><mo>*</mo><msup><mi>b22</mi><mi>n22</mi></msup></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aléa</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mrow><mi>s</mi><mo>*</mo><mi>a2</mi></mrow><mi>b2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mfrac><mi>a2</mi><mi>b2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>ppcm</mi><mo>(</mo><mi>dénominateur</mi><mo>(</mo><mi>f1</mi><mo>)</mo><mo>,</mo><mi>dénominateur</mi><mo>(</mo><mi>f2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>f1</mi><mo>+</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>9</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>100</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>281</mn><mn>900</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Test diag - Notions de base Question 04 : réduire une fraction aléatoire Quelle est la fraction réduite équivalente à la fraction suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #rep]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>17</mn><mo>,</mo><mn>19</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 04 : réduire une fraction aléatoire (Test diagnostique) Quelle est la fraction réduite équivalente à la fraction suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #rep]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>17</mn><mo>,</mo><mn>19</mn></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> réduction_8 Réduire l'expression suivante: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol #sol3 <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="fr">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>b</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>x</mi><mn>4</mn></msup><msup><mi>y</mi><mn>6</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol3</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> réduire 4 Réduis l'expression suivante

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>11</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>b</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>7</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> réduire 4 (copie) Réduis l'expression suivante

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>random</mi><mfenced><mfenced open="{" close="}"><mrow><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>random</mi><mfenced><mfenced open="{" close="}"><mrow><mn>11</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><mi>random</mi><mfenced><mfenced open="{" close="}"><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>=</mo><mi>random</mi><mfenced><mfenced open="{" close="}"><mrow><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn></mrow></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">c</mi></mrow></msup><mo>&#xB7;</mo><msup><mi>y</mi><mrow><mi mathvariant="normal">b</mi><mo>-</mo><mi mathvariant="normal">d</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task><task><title><math><mtext>Sheet 2</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> réduire 4_condition Réduis l'expression suivante

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>b</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>11</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Simplifier_Personne10 Simplifie cette expression algébrique.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«mo»*«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»*«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol La bonne réponse est #sol.

Démarche : x#a-#c*y#b-#d

]]> <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aléa</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup></mrow><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>d</mi></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Une seul variable Réduis l'expression suivante : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/mrow»«mrow»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«mo»=«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol Il faut faire «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>x</mi><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>10</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Multiple de 3 Vrai ou faux.

Ce nombre est un multiple de 3.

#n1

]]> 1.0000000 1.0000000 0 vrai faux <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10000</mn><mo>,</mo><mn>100000</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>on</mi><mo> </mo><mi>vérifie</mi><mo> </mo><mi>si</mi><mo> </mo><mi>le</mi><mo> </mo><mi>nombre</mi><mo> </mo><mi>est</mi><mo> </mo><mi>divisible</mi><mo> </mo><mi>par</mi><mo> </mo><mn>0</mn><mo> </mo><mi>avec</mi><mo> </mo><mi>la</mi><mo> </mo><mi>fonction</mi><mo> </mo><mo>&quot;</mo><mi>remainder</mi><mo>&quot;</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>rem</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>3</mn><mo>)</mo><mo>==</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mi>vrai</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>faux</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16550</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>faux</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option><option name="decimal_separator">,</option></options><localData><data name="casSession"/></localData></question> Q2 - Nombre_premier Vrai ou faux.  Le nombre suivant est premier.

#n

]]> 1.0000000 1.0000000 0 vrai faux <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>prime</mi><mo>?</mo><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mi>vrai</mi><mo>&quot;</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>&quot;</mo><mi>faux</mi><mo>&quot;</mo></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="casSession"></data></localData></question> Test diag - Notions de base $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes/1.1.2 - Addition, soustraction de polynômes Addition_monômes_xy-3 Quelle expression correspond à la somme ci-dessous?

#p1 + #p2

]]> En algèbre, lorsque l'on additionne des expressions algébriques, il faut additionner ensemble les termes semblables.

Ici, nous avons deux monômes de degré #de.

Pour effectuer l'addition: #p1 + #p2, il suffit d'additionner ensemble les coefficients numériques.

Ainsi:                        #p1 + #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>e1</mi><mo>+</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_polynômes_xy-1 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_polynômes-1 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes/1.1.3 - Multiplication de polynômes Q1 - SimpPoly3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV2__SimpPoly3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q2 - SimpPoly7 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV2__SimpPoly7.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q3 - SimpPoly9 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV2__SimpPoly9.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q4 - SimpPoly6 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV2__SimpPoly6.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q5 - SimpPoly2 1.0000000 0.0000000 0 local__jonathan__MaNTS4__DEV2__SimpPoly2.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q6 - AdSousMultPoly3 1.0000000 0.0000000 0 local__jonathan__MaNTS4__MEP212__AdSousMultPoly3.pg 1.0 0 0 0 0 0 OpaqueServer 60 https://webwork213.cegepmontpetit.ca/opaqueserver_wsdl https://webwork213.cegepmontpetit.ca/webwork2/daemon_course Q1-Multiplication 2 monômes Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q2-Multiplication_2bino-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>+</mo><mi>c4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q3-Multiplication_2bino-2 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup><mo>+</mo><mi>c4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.1 - Opérations sur les polynômes/1.1.4 - Division d'un polynôme par un monôme Polynôme_division-1 Détermine la bonne réponse à la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>p1</mi><mo>.</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>2</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfenced><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>.</mo><mn>2</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>.</mo><mn>3</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>.</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Polynôme_division-1 Effectue la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Polynôme_division-2 Effectue la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1 - Devoirs sur l'algèbre $course$/top/CSSBE/Sec 4/Algèbre/1 - Devoirs sur l'algèbre/1.1 - Opérations sur les polynômes ]]> Algèbre_vocabulaire-2 Complète le tableau en choisissant le nom associé à chaque expression algébrique.


Expression      
Nom
#p1 {#1}
#p2 {#2}
#p3 {#3}
#p4 {#4}


]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad11</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad21</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad12</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad22</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad13</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad23</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad14</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad24</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms><mo>,</mo><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>trinôme</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q1 - Algèbre_vocabulaire Complète le tableau en choisissant le nom associé à chaque expression algébrique.


Expression      
Nom
#p1 {#1}
#p2 {#2}
#p3 {#3}
#p4 {#4}


]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>monôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>binôme</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>trinôme</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad11</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad21</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad12</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad22</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad13</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad23</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>Lsol</mi><mo>.</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad14</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad24</mi><mo>=</mo><msub><mi>Lsol</mi><mrow><mi>j</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms><mo>,</mo><ms>monôme</ms><mo>,</mo><ms>binôme</ms><mo>,</mo><ms>trinôme</ms></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>trinôme</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.1 - Nombre de termes et degré d'un polynôme Q3 - Algèbre_vocabulaire_degré Donne le degré de chaque expression algébrique.


Expression     
 Degré
#p11 {#1}
#p21 {#2}
#p31 {#3}
#p41 {#4}



]]> Feedback

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>e</mi><mo>+</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>+</mo><mn>2</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>j</mi></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi><mo>,</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>p3</mi><mo>,</mo><mi>p4</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>L</mi><mo>.</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><msub><mi>L</mi><mrow><mi>k</mi><mo>+</mo><mn>3</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p11</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p31</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>degree</mi><mo>(</mo><mi>p41</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>,</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>,</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lsol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.1 - Nombre de termes et degré d'un polynôme Addition_monômes-2[ID:testP4] Quelle expression complète l'égalité ci-dessous:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mo»?«/mo»«mo»?«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»


]]> À toute addition correspond toujours deux soustractions.  Illustrons ceci avec un exemple numérique.

On a:      #a + #b = #c  et aussi:     #c - #b = #a   et    #c - #a = #b

C'est la même chose en algèbre.

Pour déterminer le terme manquant dans l'addition, il suffit de soustraire #p1 à  #p2.

Ainsi:                        «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»   Soustraire un polynôme revient à additionner l'opposé de chacun de ses termes

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»31«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»32«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»       #com1

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>e2</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p31</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>p31</mi><mo>=</mo><mo>-</mo><mi>a1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p32</mi><mo>=</mo><mi>b1</mi></mrow><mrow><mi>p32</mi><mo>=</mo><mo>-</mo><mi>b1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mi>Ici</mi><mo> </mo><msup><mi>x</mi><mn>0</mn></msup><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>est</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>nécessaire</mi><mo> </mo><mo>:</mo><mo>)</mo><mo>&quot;</mo></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup><mo>+</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>com1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ici</ms><mo> </mo><msup><ms>x</ms><mn>0</mn></msup><ms>n&apos;est</ms><mo> </mo><ms>pas</ms><mo> </mo><ms>nécessaire</ms><mo> </mo><ms>:)</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_monômes-2[ID:testP4] Quelle expression complète l'égalité ci-dessous:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mo»?«/mo»«mo»?«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»


]]> À toute addition correspond toujours deux soustractions.  Illustrons ceci avec un exemple numérique.

On a:      #a + #b = #c  et aussi:     #c - #b = #a   et    #c - #a = #b

C'est la même chose en algèbre.

Pour déterminer le terme manquant dans l'addition, il suffit de soustraire #p1 à  #p2.

Ainsi:                        «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»   Soustraire un polynôme revient à additionner l'opposé de chacun de ses termes

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»31«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»32«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»       #com1

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>e2</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p31</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>p31</mi><mo>=</mo><mo>-</mo><mi>a1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p32</mi><mo>=</mo><mi>b1</mi></mrow><mrow><mi>p32</mi><mo>=</mo><mo>-</mo><mi>b1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mi>Ici</mi><mo> </mo><msup><mi>x</mi><mn>0</mn></msup><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>est</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>nécessaire</mi><mo> </mo><mo>:</mo><mo>)</mo><mo>&quot;</mo></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup><mo>+</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>com1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ici</ms><mo> </mo><msup><ms>x</ms><mn>0</mn></msup><ms>n&apos;est</ms><mo> </mo><ms>pas</ms><mo> </mo><ms>nécessaire</ms><mo> </mo><ms>:)</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_périmètre Détermine l'expression algébrique représentant le périmètre du rectangle ci-dessous.

#plotter1

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>&quot;</mo><mi>arrow_xy</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr1</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>polygon</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr1</mi><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>+</mo><mi>p2</mi></mrow></mfenced><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>.</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>19</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">×</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_périmètre_rectangle Détermine l'expression algébrique représentant l'aire du rectangle ci-dessous.

#plotter1

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>&quot;</mo><mi>arrow_xy</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr1</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>polygon</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr1</mi><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>+</mo><mi>p2</mi></mrow></mfenced><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>.</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>43</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">×</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q10 - Addition_monômes_compléter Quelle expression complète l'égalité ci-dessous:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mo»?«/mo»«mo»?«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»


]]> À toute addition correspond toujours deux soustractions.  Illustrons ceci avec un exemple numérique.

On a:      #a + #b = #c  et aussi:     #c - #b = #a   et    #c - #a = #b

C'est la même chose en algèbre.

Pour déterminer le terme manquant dans l'addition, il suffit de soustraire #p1 à  #p2.

Ainsi:                        «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»   Soustraire un polynôme revient à additionner l'opposé de chacun de ses termes

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»31«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»32«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»11«/mn»«/mrow»«/msup»«/math»       #com1

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b1</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>e2</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p31</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>p31</mi><mo>=</mo><mo>-</mo><mi>a1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p32</mi><mo>=</mo><mi>b1</mi></mrow><mrow><mi>p32</mi><mo>=</mo><mo>-</mo><mi>b1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mi>Ici</mi><mo> </mo><msup><mi>x</mi><mn>0</mn></msup><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>est</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>nécessaire</mi><mo> </mo><mo>:</mo><mo>)</mo><mo>&quot;</mo></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e1</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo> </mo><mi>e11</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow><mrow><mi>e11</mi><mo>=</mo><mi>e1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a1</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mi>b2</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>com1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ici</ms><mo> </mo><msup><ms>x</ms><mn>0</mn></msup><ms>n&apos;est</ms><mo> </mo><ms>pas</ms><mo> </mo><ms>nécessaire</ms><mo> </mo><ms>:)</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q11 - Addition_binômes_compléter Quelle expression complète l'égalité ci-dessous:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mo»?«/mo»«mo»?«/mo»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»


]]> À toute addition correspond toujours deux soustractions.  Illustrons ceci avec un exemple numérique.

On a:      #a + #b = #c  et aussi:     #c - #b = #a   et    #c - #a = #b

C'est la même chose en algèbre.

Pour déterminer le terme manquant dans l'addition, il suffit de soustraire #p1 à  #p2.

Ainsi:                        «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»   Soustraire un polynôme revient à additionner l'opposé de chacun de ses termes

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»31«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»32«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»11«/mn»«/mrow»«/msup»«/math»       #com1

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>e2</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mi>b2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p31</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>p31</mi><mo>=</mo><mo>-</mo><mi>a1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>p32</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>b1</mi></mfenced></mrow><mrow><mi>p32</mi><mo>=</mo><mo>-</mo><mi>b1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e11</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mi>Ici</mi><mo> </mo><msup><mi>x</mi><mn>0</mn></msup><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>est</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>nécessaire</mi><mo> </mo><mo>:</mo><mo>)</mo><mo>&quot;</mo></mrow><mrow><mi>com1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e1</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>e11</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p2</mi><mo>-</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>+</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e2</mi></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e2</mi></mrow></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p311</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>com1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Ici</ms><mo> </mo><msup><ms>x</ms><mn>0</mn></msup><ms>n&apos;est</ms><mo> </mo><ms>pas</ms><mo> </mo><ms>nécessaire</ms><mo> </mo><ms>:)</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q16 - Addition_périmètre Détermine l'expression algébrique représentant le périmètre du rectangle ci-dessous.

#plotter1

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>&quot;</mo><mi>arrow_xy</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr1</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>polygon</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr1</mi><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>+</mo><mi>p2</mi></mrow></mfenced><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>.</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>19</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">×</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q2 - Révision_mônomes monômes.
]]> 1.0000000 0.3333333 0 false true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #p1

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>.</mo><mn>30</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>8</mn><mn>7</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><msup><mi>b</mi><mn>3</mn></msup><mo>*</mo><msup><mi>c</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>8</mn><mn>7</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mfrac><mn>8</mn><mn>9</mn></mfrac><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p8</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>21</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.1 - Nombre de termes et degré d'un polynôme Q23 - Multiplication_périmètre_rectangle Détermine l'expression algébrique représentant l'aire du rectangle ci-dessous.

#plotter1

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WH</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>WW</mi><mo>=</mo><mn>400</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>:</mo><mo>=</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>:</mo><mo>=</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w3</mi><mo>:</mo><mo>=</mo><mi>window_height</mi><mo>=</mo><mi>WH</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w4</mi><mo>:</mo><mo>=</mo><mi>window_width</mi><mo>=</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w5</mi><mo>:</mo><mo>=</mo><mi>window_aspect_ratio</mi><mo>=</mo><mi>WH</mi><mo>/</mo><mi>WW</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w6</mi><mo>:</mo><mo>=</mo><mi>axis_color</mi><mo>=</mo><mi>black</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w7</mi><mo>:</mo><mo>=</mo><mi>grid_color</mi><mo>=</mo><mi>green</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w8</mi><mo>:</mo><mo>=</mo><mi>axis_style</mi><mo>=</mo><mo>&quot;</mo><mi>arrow_xy</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w9</mi><mo>:</mo><mo>=</mo><mi>axis_label</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w2</mi><mo>,</mo><mi>w3</mi><mo>,</mo><mi>w4</mi><mo>,</mo><mi>w5</mi><mo>,</mo><mi>w6</mi><mo>,</mo><mi>w7</mi><mo>,</mo><mi>w8</mi><mo>,</mo><mi>w9</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tr1</mi><mo>=</mo><mi>plotter</mi><mo>(</mo><mi>point</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>,</mo><mi>W</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>:</mo><mo>=</mo><mi>point</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pol1</mi><mo>=</mo><mi>polygon</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>tr1</mi><mo>,</mo><mi>pol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blue</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>+</mo><mi>p2</mi></mrow></mfenced><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>8</mn><mo>.</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>write</mi><mo>(</mo><mi>p2</mi><mo>,</mo><mi>point</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>43</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">×</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q26 - Polynôme_division Détermine la bonne réponse à la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

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]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>p1</mi><mo>.</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>2</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>3</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfenced><mfrac><mrow><mi>p1</mi><mo>.</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>p1</mi><mo>.</mo><mn>1</mn></mrow><mrow><mi>p2</mi><mo>.</mo><mn>1</mn></mrow></mfrac></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>.</mo><mn>2</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>.</mo><mn>3</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>.</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.4 - Division d'un polynôme par un monôme Q7 - Soustraction_monômes Quelle expression correspond à la différence ci-dessous?

#p1 - #p2

]]> En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q8 - Soustraction_monômes_xy Quelle expression correspond à la somme ci-dessous?

#p1 - #p2

]]>

En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #de.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»§#183;«/mo»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>de</mi><mo>=</mo><mi>e1</mi><mo>+</mo><mi>e2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Révision_mônomes[ID:revision]_nolink monômes.
]]> 1.0000000 0.3333333 0 false true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #p1

]]> #p2

]]> #p3

]]> #p4

]]> #p5

]]> #p6 #p7

]]> #p8

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mi>a</mi><mi>b</mi></mfrac><mo> </mo><mi>with</mi><mo> </mo><mi>a</mi><mo>,</mo><mi>b</mi><mo> </mo><mi>in</mi><mo> </mo><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>,</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math 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name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_monômes-2 Quelle expression correspond à la différence ci-dessous?

#p1 - #p2

]]> En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_monômes-2 Quelle expression correspond à la différence ci-dessous?

#p1 - #p2

]]> En algèbre, lorsque l'on soustraie des monômes semblables, il faut soustraire leurs coefficients numériques.

Ici, nous avons deux monômes de degré #e1.

Pour effectuer la soustraction : #p1 - #p2, il suffit de soustraire  les coefficients numériques.

Ainsi:                        #p1 - #p2

                               = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

                               = #sol 

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>b</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>e1</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Terme algébrique-1[ID:terme] Détermine, parmi les expressions suivantes, celles qui représentent un terme algébrique.

]]> 1.0000000 0.3333333 0 false true none ]]> Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol1
 

]]> Bravo!
 

]]> #sol2
 

]]> Bravo!

]]> #sol3
 

]]> Bravo!

]]> #bad1
 

]]> Cette expression contient une addition de deux termes algébriques que l'on ne peut simplifié.

]]> #bad2
 

]]> Cette expression contient une soustraction de deux termes algébriques que l'on ne peut simplifié.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»
 

]]> Lorsque simplifiée, cette expressions contient 3 termes algébriques: #bad3

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/msup»«/math»
 

]]> L'expression contient une variable au numérateur qui est affectée d'un exposant négatif.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mfrac bevelled=¨true¨»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/msup»«/math»
 

]]> La variable x est affectée d'un exposant fractionnaire

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>j</mi><mi>i</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>j</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><mi>j</mi><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>j</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>j</mi><mo>+</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow></msup><mo>-</mo><mi>s</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>s</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mo>(</mo><mi>p1</mi><mo>+</mo><mi>k1</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_plus complexe-2(avec restrictions) (copie) Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>30</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>72</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>56</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_polynômes Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_polynômes_xy-1 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_polynômes_xy-2 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> alg_ME-1 (accepte des réponses comme 1(4a+16), 2(2a +16) ) Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fac</mi><mo>=</mo><mi>gcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Binômes_trouver_addition-1 Donne deux binômes dont la somme est égale à:

#p

]]> 1.0000000 0.3333333 0 0 p1=#p1p2=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>repeat</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>0</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup><mspace linebreak="newline" indentshift="0"/><mi>until</mi><mo>&#xA0;</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>3</mn></mrow></mfenced><mo>&#x2260;</mo><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>&#xB7;</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>&#xB7;</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command name="simplify"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>&#xB7;</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn></math></output></command><command name="simplify"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>&#xB7;</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Binômes_trouver_addition-2 Donne deux binômes dont la somme est égale à : 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 p1x=#p1p2x=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>null</mi><mo>↦</mo><mi>random</mi><mo>⁡</mo><mfenced><mfrac><mfenced close="]" open="["><mrow><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><mo>..</mo><mn>5</mn></mrow></mfenced><mfenced close="]" open="["><mn>0</mn></mfenced></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>1</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Binômes_trouver_addition-3 Donne deux binômes dont la somme est égale à : 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 p1x=#p1p2x=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>null</mi><mo>↦</mo><mi>random</mi><mo>⁡</mo><mfenced><mfrac><mfenced close="]" open="["><mrow><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><mo>..</mo><mn>5</mn></mrow></mfenced><mfenced close="]" open="["><mn>0</mn></mfenced></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>1</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Binômes_trouver_addition-3 Donne deux binômes dont la somme est égale à : 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 p1x=#p1p2x=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>null</mi><mo>↦</mo><mi>random</mi><mo>⁡</mo><mfenced><mfrac><mfenced close="]" open="["><mrow><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><mo>..</mo><mn>5</mn></mrow></mfenced><mfenced close="]" open="["><mn>0</mn></mfenced></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>1</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Division_plus complexe-3(avec restrictions et négatifs) (copie) Effectue la division demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Multiplication_2bino-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>+</mo><mi>c4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_2bino-2 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup><mo>+</mo><mi>c4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_2monomes-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_2monomes-2 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>56</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_2tri-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_bino^2-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_bino^2-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>50</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_bino^2-2 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>+</mo><mi>c4</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_bino_tri-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>67</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_mon_bino-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_mono_tri-1 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_plus complexe-2(avec restrictions avec négatifs) (copie) Effectue la multiplication demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn><mtext xml:lang="en">variables</mtext></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Polynôme_division-1 Effectue la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Polynôme_division-2 Effectue la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q12 - Monômes_trouver_addition Écris deux monômes non nuls dont la somme est égale à:

#p

]]> 1.0000000 0.3333333 0 0 premier monôme=#p1deuxième monôme=#p2]]> #c1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r</mi><mo> </mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable><mrow><mi>r</mi><mo>≠</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>j</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>u</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>∧</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>,</mo><mo> </mo><mi>vous</mi><mo> </mo><mi>avez</mi><mo> </mo><mi>réussi</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>des</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nulles</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>devez</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>avez</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>entré</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>u</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>∧</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>,</mo><mo> </mo><mi>vous</mi><mo> </mo><mi>avez</mi><mo> </mo><mi>réussi</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>u</mi><mo>==</mo><mn>0</mn><mo>∧</mo><mi>v</mi><mo>==</mo><mn>0</mn></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>des</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nulles</mi><mo>&quot;</mo></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>devez</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>u</mi><mo>==</mo><mn>0</mn><mo>∨</mo><mi>v</mi><mo>==</mo><mn>0</mn><mo>)</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>avez</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>entré</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo> </mo><mi>m</mi><mi>o</mi><mi>n</mi><mi>ô</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>è</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>m</mi><mi>o</mi><mi>n</mi><mi>ô</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q13 - Binômes_trouver_addition Donne deux binômes dont la somme est égale à : 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 p1x=#p1p2x=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>null</mi><mo>↦</mo><mi>random</mi><mo>⁡</mo><mfenced><mfrac><mfenced close="]" open="["><mrow><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><mo>..</mo><mn>5</mn></mrow></mfenced><mfenced close="]" open="["><mn>0</mn></mfenced></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>1</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>2</mn></mrow></mfenced><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mfenced><mi>x</mi></mfenced><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q14 - Binômes_trouver_addition Donne deux binômes dont la somme est égale à :

#p

]]> #c1

]]> 1.0000000 0.3333333 0 0 premier binôme=#p1deuxième binôme=#p2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>leading_coefficient</mi><mo>(</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>≠</mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable><mrow><mi>r</mi><mo>≠</mo><mi>j</mi><mo>∧</mo><mi>s</mi><mo>≠</mo><mo>-</mo><mi>k</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>leading_coefficient</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>leading_coefficient</mi><mo>(</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mo>(</mo><mi>s</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>j</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mo>-</mo><mi>k</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>,</mo><mo> </mo><mi>vous</mi><mo> </mo><mi>avez</mi><mo> </mo><mi>réussi</mi><mo>!</mo><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Relis</mi><mo> </mo><mi>bien</mi><mo> </mo><mi>la</mi><mo> </mo><mi>question</mi><mo>,</mo><mo> </mo><mi>il</mi><mo> </mo><mi>y</mi><mo> </mo><mi>a</mi><mo> </mo><mi>une</mi><mo> </mo><mi>infinité</mi><mo> </mo><mi>de</mi><mo> </mo><mi>réponses</mi><mo>!</mo><mo>&quot;</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo> </mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>ô</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>è</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>ô</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q15 - Binômes_trouver_addition Donne deux binômes dont la somme est égale à:

#p

]]> 1.0000000 0.3333333 0 0 p1=#p1p2=#p2]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="lang">en</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>repeat</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">p</mi><mo>=</mo><munderover wrs:positionable="false"><mo>&#x2211;</mo><mrow><mrow wrs:positionable="true"><mi>i</mi></mrow><mo>==</mo><mrow wrs:positionable="true"><mn>0</mn></mrow></mrow><mrow wrs:positionable="true"><mn>2</mn></mrow></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup><mspace linebreak="newline" indentshift="0"/><mi>until</mi><mo>&#xA0;</mo><mi>term</mi><mfenced><mrow><mi mathvariant="normal">p</mi><mo>,</mo><mn>3</mn></mrow></mfenced><mo>&#x2260;</mo><mo>-</mo><mn>1</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>&#xB7;</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>&#xB7;</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command name="simplify"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><mi>term</mi><mfenced><mrow><mi 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>begin</mi><mspace linebreak="newline" indentshift="1"/><mi>if</mi><mo>&#xA0;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#x2227;</mo><mi>n_terms</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>==</mo><mn>2</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="3"/><mi>credit</mi><mo>=</mo><mn>1</mn><mspace linebreak="newline" indentshift="2"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>else_if</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">y</mi><mo>==</mo><mi mathvariant="normal">p</mi><mo>&#xA0;</mo><mo>&#x2227;</mo><mi mathvariant="normal">x</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#x2227;</mo><mi mathvariant="normal">y</mi><mo>&#x2260;</mo><mn>0</mn><mo>&#xA0;</mo><mi>then</mi><mspace linebreak="newline" indentshift="2"/><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mspace linebreak="newline" indentshift="1"/><mi>end</mi><mspace linebreak="newline" indentshift="1"/><mi>return</mi><mo>&#xA0;</mo><mi>credit</mi><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>p</mi><mn>2</mn></msub><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q17 - Équation_périmètre

Le périmètre d’un rectangle est de #per cm. Sa longueur mesure #b  cm de plus que sa largeur, quelles sont les dimensions du rectangle ?

 


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Posons:

Largeur du rectangle: x

Longueur du rectangle: (x + #b)

Le périmètre du rectangle peut être représenté par:

x + (x + #b) + x + (x + #b) = #per

4x+ #b2 = #per

4x = #diff1

x = #larg

Largeur= #larg cm

Longueur = #long cm


]]> 1.0000000 0.3333333 0 0 Largeur=#largLongueur=#long]]>


]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>140</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>larg</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>long</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mo> </mo><mn>2</mn><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>diff1</mi><mo>=</mo><mo> </mo><mi>per</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>117</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>r</mi><mo>=</mo><mo>#</mo><mi>l</mi><mi>a</mi><mi>r</mi><mi>g</mi><mspace linebreak="newline"/><mi>L</mi><mi>o</mi><mi>n</mi><mi>g</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>r</mi><mo>=</mo><mo>#</mo><mi>l</mi><mi>o</mi><mi>n</mi><mi>g</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50-50</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> SAE - 1.1 - Opérations sur les polynômes Q18 - Multiplication_mon_bino Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i3</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>*</mo><msup><mi>y</mi><mi>i4</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>6</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q19 - Multiplication_mono_tri Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>27</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup><mo>-</mo><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q20 - Multiplication_bino^2 Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i3</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i4</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mi>i1</mi></msup><mo>+</mo><mi>c3</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c2</mi><mo>*</mo><msup><mi>x</mi><mi>i2</mi></msup><mo>+</mo><mi>c4</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q21 - Multiplication_bino_tri Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>28</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>67</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q22 - Multiplication_2tri Effectue la multiplication ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_polynomial_form"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.3 - Multiplication de polynômes Q24 - SAE_Algèbre Il faut mettre ici à contribution les notions d'algèbre vues en troisième secondaire.


Sachant que :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

Quelle est la valeur numérique de : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»?

]]> Il faut résoudre l'équation algébrique afin de déterminer la valeur de "x" qui sera remplacer dans «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math».

Développons:    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/math»     On peut simplifier «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» de chaque côté

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«mn»1«/mn»«/math»     Ensuite mettre les termes en "x" du même côté

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»c«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»c«/mi»«/math»  Effectuer les simplifications

                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»c«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»c«/mi»«/math»

                                           «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»5«/mn»«/math»

                                                      «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»5«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«/math»

Et on a donc: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><msup><mi>p2</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax2</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx2</mi><mo>=</mo><mi>bx</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax1</mi><mo>=</mo><mi>p11</mi><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx1</mi><mo>=</mo><mi>p21</mi><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cax</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cbx</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>ax</mi><mo>-</mo><mi>bx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bc</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi><mo>=</mo><mi>bc</mi><mo>-</mo><mi>ac</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi><mo>=</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>a</mi><mo>-</mo><mn>2</mn><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep2</mi><mo>=</mo><mi>rep</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>rep</mi><mo>+</mo><mi>c</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p1</mi><mn>2</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p2</mi><mn>2</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> SAE - 1.1 - Opérations sur les polynômes Q25 - Polynôme_division Effectue la division ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.4 - Division d'un polynôme par un monôme Q27 - Algèbre_MES Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>a</mi><mi>e</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>a</mi><mrow><mi>e</mi><mo>-</mo><mn>2</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fac</mi><mo>=</mo><mi>gcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mfenced><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.5 - Mise en évidence simple Q28 - Algèbre_MES Exprime le polynôme suivant comme un produit de facteurs.

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>f</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>g</mi></mtd></mtr></mtable><mrow><mfenced close="&verbar;" open="&verbar;"><mrow><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>c1</mi></mrow></mfenced><mo>&gt;</mo><msup><mi>b1</mi><mn>2</mn></msup></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>+</mo><mi>b1</mi><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c1</mi><mo>*</mo><msup><mi>x</mi><mrow><mi>e</mi><mo>-</mo><mn>2</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>,</mo><integers/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>12</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfenced><mrow><mfrac><msqrt><mn>13</mn></msqrt><mn>2</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mfrac><msqrt><mn>13</mn></msqrt><mn>2</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.5 - Mise en évidence simple Q29 - Division_MES Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>n</mi><mi>m</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.5 - Mise en évidence simple Q30 - Divison_MES Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>bin1</mi><mi>bin2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.5 - Mise en évidence simple Q31 - Division_MES Simplifie l'expression algébrique suivante. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #bin1x#bin2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>4</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>mon2</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>bin1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>mon1</mi><mo>*</mo><mi>bin1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>mon2</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>bin2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>56</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>#</mo><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mn>1</mn></mrow><mrow><mi>x</mi><mfenced><mrow><mo>#</mo><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mn>2</mn></mrow></mfenced></mrow></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.5 - Mise en évidence simple Q4 - Addition_polynômes Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q5 - Addition_polynômes_xy Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q6 - Addition_polynômes_xy Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Q9 - Soustraction_polynômes_xy Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.1.2 - Addition et soustraction de polynômes Question 07 : réduire fraction algébrique par MES - réponse fraction Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>n</mi><mi>m</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 07 : réduire fraction algébrique par MES - réponse fraction Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>11</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>n</mi><mi>m</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 08 : réduire fraction algébrique par MES - réponse division de 2 binôme Réduis à sa plus simple expression la fraction ci-dessous sachant que le dénominateur est différent de 0. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»o«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #ans]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi><mo>=</mo><mfrac><mi>bin1</mi><mi>bin2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ans</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 09 : réduire fraction algébrique par MES - réponse complexe Simplifie l'expression algébrique suivante. 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #bin1x#bin2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>4</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>mon2</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>bin1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>mon1</mi><mo>*</mo><mi>bin1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>mon2</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>x</mi><mo>*</mo><mi>bin2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>15</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>56</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>#</mo><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mn>1</mn></mrow><mrow><mi>x</mi><mfenced><mrow><mo>#</mo><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mn>2</mn></mrow></mfenced></mrow></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1] Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> Il suffit d'additionner les termes "semblables" ensemble.

                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»12«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»22«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»10«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»20«/mn»«/mrow»«/mfenced»«/math»

                                             = #sol

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limite</mi><mo> </mo><mi>et</mi><mo> </mo><mi>exclusion</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>coefficients</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>5</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>des</mi><mo> </mo><mi>coeficients</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Construction</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi><mo> </mo><mi>p1</mi><mo> </mo><mi>et</mi><mo> </mo><mi>p2</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>somme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p10</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p20</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1] code ne fonctionne pas MathML W3C ? Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> Il suffit d'additionner les termes "semblables" ensemble.

                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»12«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»22«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»10«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»20«/mn»«/mrow»«/mfenced»«/math»

                                             = #sol

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limite</mi><mo> </mo><mi>et</mi><mo> </mo><mi>exclusion</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>coefficients</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>5</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>des</mi><mo> </mo><mi>coeficients</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Construction</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi><mo> </mo><mi>p1</mi><mo> </mo><mi>et</mi><mo> </mo><mi>p2</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>somme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p10</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p20</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1]_lien_mp4 Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]>

Solution

Puisqu'on a ici une somme de polynômes, pour simplifier les calculs il suffit d'additionner ensemble les termes "semblables"      

L'addition: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#160;«/mo»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»                                                                                                                  

se fait comme suit terme à terme:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

Ce qui donne:

#sol

]]> 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1.0000000 0.3333333 0 0 #sol]]> ]]> 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 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limite</mi><mo> </mo><mi>et</mi><mo> </mo><mi>exclusion</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>coefficients</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>5</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>des</mi><mo> </mo><mi>coeficients</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Construction</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi><mo> </mo><mi>p1</mi><mo> </mo><mi>et</mi><mo> </mo><mi>p2</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c2</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>somme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1]_lien_mp4 Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

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Puisqu'on a ici une somme de polynômes, pour simplifier les calculs il suffit d'additionner ensemble les termes "semblables"     

L'addition: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#160;«/mo»«/mrow»«/mfenced»«mo»+«/mo»«mo»§#160;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»                                                                                                                 

se fait comme suit terme à terme:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

Ce qui donne:

#sol

Aide




]]> 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1.0000000 0.3333333 0 0 #sol]]> ]]> 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 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>limite</mi><mo> </mo><mi>et</mi><mo> </mo><mi>exclusion</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>les</mi><mo> </mo><mi>coefficients</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>5</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>des</mi><mo> </mo><mi>coeficients</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Construction</mi><mo> </mo><mi>des</mi><mo> </mo><mi>polynômes</mi><mo> </mo><mi>p1</mi><mo> </mo><mi>et</mi><mo> </mo><mi>p2</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c2</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Calcul</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>somme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1a]_français Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> Il faut faire l'addition terme à terme pour obtenir la bonne réponse.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»12«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»22«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»10«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»20«/mn»«/mrow»«/mfenced»«/math»

#sol

Cliquez pour plus d'infos

]]> 1.0000000 0.3333333 0 0 #sol 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<question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aléa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1a]_français Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> Il faut faire l'addition terme à terme pour obtenir la bonne réponse.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»12«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»22«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»10«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«mn»20«/mn»«/mrow»«/mfenced»«/math»

#sol

Cliquez pour plus d'infos

]]> 1.0000000 0.3333333 0 0 #sol 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 <question><wirisCasSession><![CDATA[<session lang="fr" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aléa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p10</mi><mo>=</mo><mi>p1</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p20</mi><mo>=</mo><mi>p2</mi><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1b]_français_html5 Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>==</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>==</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task><task><title><math><mtext>Feuille 2</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo></math></input></command></group></task></session></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_addition[ID:test1b]_français_html5 Effectue la somme des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mfenced open="[" close="]"><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced open="[" close="]"><mn>0</mn></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>==</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>i</mi><mo>==</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi mathvariant="normal">r</mi><mfenced><mrow/></mfenced><mo>&#xB7;</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>+</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task><task><title><math><mtext>Feuille 2</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo></math></input></command></group></task></session></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Révision algèbre_soustraction[ID:test3] Effectue la soustraction des polynômes ci-dessous.  Donne une réponse simplifiée.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> SAE_Algèbre Il faut mettre ici à contribution les notions d'algèbre vues en troisième secondaire.


Sachant que :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

Quelle est la valeur de : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»?

]]> Il faut résoudre l'équation algébrique afin de déterminer la valeur de "x" qui sera remplacer dans «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math».

Développons:    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»11«/mn»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/math»     On peut simplifier «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» de chaque côté

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«mn»1«/mn»«/math»     Ensuite mettre les termes en "x" du même côté

                                «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»c«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»c«/mi»«/math»  Effectuer les simplifications

                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mi»x«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mi»c«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»c«/mi»«/math»

                                           «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«mn»5«/mn»«/math»

                                                      «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»5«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«/math»

Et on a donc: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><msup><mi>p1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><msup><mi>p2</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax2</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx2</mi><mo>=</mo><mi>bx</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax1</mi><mo>=</mo><mi>p11</mi><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx1</mi><mo>=</mo><mi>p21</mi><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cax</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cbx</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>ax</mi><mo>-</mo><mi>bx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bc</mi><mo>=</mo><mi>p21</mi><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi><mo>=</mo><mi>bc</mi><mo>-</mo><mi>ac</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep</mi><mo>=</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>a</mi><mo>-</mo><mn>2</mn><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rep2</mi><mo>=</mo><mi>rep</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>rep</mi><mo>+</mo><mi>c</mi><msup><mo>)</mo><mn>2</mn></msup><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p1</mi><mn>2</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>p2</mi><mn>2</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_polynômes_xy-2 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mrow><mi>s</mi><mo>(</mo><mo>)</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_polynômes-1 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_polynômes-2 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_polynômes-2 Effectue l'addition ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>*</mo><msup><mi>y</mi><mi>s</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>p2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>-</mo><mn>11</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> SP_1.1 somme de 2 monômes[ID:SP1] Écris deux monômes non nuls dont la somme est égale à:

#p

]]> 1.0000000 0.3333333 0 0 premier monôme=#p1deuxième monôme=#p2]]> #c1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r</mi><mo> </mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable><mrow><mi>r</mi><mo>≠</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>j</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>u</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>∧</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>,</mo><mo> </mo><mi>vous</mi><mo> </mo><mi>avez</mi><mo> </mo><mi>réussi</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>des</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nulles</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>devez</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>avez</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>entré</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∧</mo><mi>u</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>not_null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>∧</mo><mi>v</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>,</mo><mo> </mo><mi>vous</mi><mo> </mo><mi>avez</mi><mo> </mo><mi>réussi</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>u</mi><mo>==</mo><mn>0</mn><mo>∧</mo><mi>v</mi><mo>==</mo><mn>0</mn></mrow><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>des</mi><mo> </mo><mi>valeurs</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nulles</mi><mo>&quot;</mo></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>u</mi><mo>)</mo><mo>∨</mo><mi>null</mi><mo>?</mo><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo><mo>∧</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>devez</mi><mo> </mo><mi>entrer</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>u</mi><mo>==</mo><mn>0</mn><mo>∨</mo><mi>v</mi><mo>==</mo><mn>0</mn><mo>)</mo><mo>(</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>==</mo><mi>p1</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Vous</mi><mo> </mo><mi>n</mi><mo>&apos;</mo><mi>avez</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>entré</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>monômes</mi><mo> </mo><mi>non</mi><mo> </mo><mi>nuls</mi><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit</mi></mtd></mtr></mtable></apply></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>z</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo>&#xA0;</mo><mi>m</mi><mi>o</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>&#xE8;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>m</mi><mi>o</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> SP_1.2 somme de 2 binômes[ID:SP2.1] (copie) Donne deux binômes dont la somme est égale à:

#p

]]> #c1

]]> 1.0000000 0.3333333 0 0 premier binôme=#p1deuxième binôme=#p2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mrow><mrow><mi>r</mi><mo>≠</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow></mfenced></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow></mfenced></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>donner</mi><mo> </mo><mn>2</mn><mo> </mo><mi>binômes</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>avoir</mi><mo> </mo><mi>tous</mi><mo> </mo><mi>les</mi><mo> </mo><mi>points</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>revoir</mi><mo> </mo><mi>tes</mi><mo> </mo><mi>notions</mi><mo> </mo><mi>d</mi><mo>&apos;</mo><mi>algèbre</mi><mo>&quot;</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit1</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>credit1</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit1</mi></mtd></mtr></mtable></apply></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>&#xE8;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> SP_1.2 somme de 2 binômes[ID:SP2.1] (copie) Donne deux binômes dont la somme est égale à:

#p

]]> #c1

]]> 1.0000000 0.3333333 0 0 premier binôme=#p1deuxième binôme=#p2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mrow><mrow><mi>r</mi><mo>≠</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup><mo>+</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow></mfenced></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Bravo</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow></mfenced></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>donner</mi><mo> </mo><mn>2</mn><mo> </mo><mi>binômes</mi><mo> </mo><mi>pour</mi><mo> </mo><mi>avoir</mi><mo> </mo><mi>tous</mi><mo> </mo><mi>les</mi><mo> </mo><mi>points</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>c1</mi><mo>=</mo><mo>&quot;</mo><mi>Il</mi><mo> </mo><mi>faut</mi><mo> </mo><mi>revoir</mi><mo> </mo><mi>tes</mi><mo> </mo><mi>notions</mi><mo> </mo><mi>d</mi><mo>&apos;</mo><mi>algèbre</mi><mo>&quot;</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit1</mi></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>credit1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_terms</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>credit1</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>u</mi><mo>+</mo><mi>v</mi><mo>=</mo><mi>p</mi></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>=</mo><mi>credit1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>7</mn></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>credit1</mi></mtd></mtr></mtable></apply></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>&#xE8;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> SP_1.2 somme de 2 binômes[ID:SP2] Donne deux binômes dont la somme est égale à :

#p

]]> #c1

]]> 1.0000000 0.3333333 0 0 premier binôme=#p1deuxième binôme=#p2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>leading_coefficient</mi><mo>(</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>≠</mo><mi>j</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable><mrow><mi>r</mi><mo>≠</mo><mi>j</mi><mo>∧</mo><mi>s</mi><mo>≠</mo><mo>-</mo><mi>k</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>p</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></mtd></mtr></mtable></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>leading_coefficient</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>leading_coefficient</mi><mo>(</mo><mi>term</mi><mo>(</mo><mi>p</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>r</mi><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mo>(</mo><mi>s</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>j</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mi>a</mi></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup><mo>+</mo><mo>-</mo><mi>k</mi><mo>*</mo><mi>L</mi><mo>.</mo><msup><mi>i</mi><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><mi>L</mi><mo>.</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol 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actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"/></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>u</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>&#xE8;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>b</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>&#xF4;</mi><mi>m</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1 - Devoirs sur l'algèbre/1.2 - Factorisation Q18 - Facto fraction algébrique Sachant que les dénominateurs sont différents de 0, quelle expression algébrique est équivalente à l'expression algébrique ci-dessous? 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»o«/mi»«mi»l«/mi»«mi»y«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

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]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poly</mi><mo>=</mo><mi>bin1</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>bin1</mi><mo>*</mo><mi>bin3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>poly</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>x</mi><mo>-</mo><mn>12</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Simplification de fractions algébriques Q19 - Facto fraction algébrique Sachant que le dénominateur est différent de 0, quelle expression algébrique est équivalente à l'expression ci-dessous. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

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]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>4</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>b</mi></mfenced></mrow></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Le</mi><mo> </mo><mi>fait</mi><mo> </mo><mi>d</mi><mo>&apos;</mo><mi>enlever</mi><mo> </mo><mi>b</mi><mo> </mo><mi>assure</mi><mo> </mo><mi>que</mi><mo> </mo><mi>ce</mi><mo> </mo><mi>soit</mi><mo> </mo><mi>un</mi><mo> </mo><mi>trinôme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin1</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin3</mi><mo>*</mo><mi>bin4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>49</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>588</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Simplification de fractions algébriques Q20 - Facto fraction algébrique Sachant que le dénominateur est différent de 0, quelle expression algébrique est équivalente à l'expression ci-dessous. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct.

]]> Your answer is partially correct.

]]> Your answer is incorrect.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>6</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>4</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>b</mi></mfenced></mrow></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Enlever</mi><mo> </mo><mi>b</mi><mo> </mo><mi>assure</mi><mo> </mo><mi>que</mi><mo> </mo><mi>ce</mi><mo> </mo><mi>soit</mi><mo> </mo><mi>un</mi><mo> </mo><mi>trinôme</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>bin1</mi><mo>*</mo><mi>bin2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>bin2</mi><mo>*</mo><mi>bin4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>378</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Simplification de fractions algébriques DME-1_(ax^2-b)(cy-d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax^2-b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax^2+b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax-b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mo>(</mo><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax-b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mo>(</mo><mo>-</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax+b)(cy+d)_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax+b)(cy+d)_Réordonner Factorise le polynôme ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»q«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»q«/mi»«mn»2«/mn»«/math»

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme. Aussi, dans ce cas, il faut réorganiser les termes avant d'effectuer la factorisation.  En inversant le deuxième et le troisième terme, la double mise en évidence devient possible.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>,</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>+</mo><mn>6</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>*</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>*</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_(ax+b)(cy+d)_Réordonner Factorise le polynôme ci-dessous.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»q«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»q«/mi»«mn»2«/mn»«/math»

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme. Aussi, dans ce cas, il faut réorganiser les termes avant d'effectuer la factorisation.  En inversant le deuxième et le troisième terme, la double mise en évidence devient possible.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>,</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>+</mo><mn>6</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>*</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>*</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_coeff_(ax-b)(cy+d) Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

#p1

#p2





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Coefficients</mi><mo> </mo><mi>positifs</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-1_R Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>a</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>a</mi></mfenced><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> DME-2(ax-b)(cx-d) Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

#p1

#p2





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_x^2+bx+x_2[ID:facto_2] Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_x^2+bx+x_2[ID:facto_3] Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_x^2+bx+x_2[ID:facto_4] Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>=</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_x^2+bx+x_2[ID:facto_5] Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>=</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Facto_x^2+bx+x_2[ID:facto_5] Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>=</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q1 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>a</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>a</mi></mfenced><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>*</mo><mfenced close="&verbar;" open="&verbar;"><mi>c</mi></mfenced><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>-</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q10 - TSP Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.3 - Trinôme somme-produit Q11 - TSP Factorise le polynôme ci-dessous.

#p1

]]> On a ici un polynôme de la forme: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math».

Il faut trouver deux nombres dont le produit est #p et dont la somme égale #s1 . Ces deux nombres sont: #a et #b.

La factorisation de #p1 est dont #sol.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mi>a</mi><mo>≠</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.3 - Trinôme somme-produit Q12 - TSP Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.3 - Trinôme somme-produit Q13 - TCP Factorise le polynôme suivant:

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.4 - Trinôme carré parfait Q14 - TCP Factorise le polynôme suivant:

#p1

]]>

Nous avons ici un trinôme carré parfait.

En effet,

#c1 est le carré de #c3

#c2 correspond au carré de #b

et #dp est le double produit de #c3 par #b.

La factorisation est donc: #sol


]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mo>(</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dp</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>140</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.4 - Trinôme carré parfait Q15 - TCC Factorise l'expression algébrique suivante:

#p2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>13</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille de calculs</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="cas">add</data></localData></question> 1.2.5 - Trinôme complétion du carré Q16 - TCC Factorise le polynôme suivant:

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mo> </mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mo> </mo><mi>a2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>som1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.5 - Trinôme complétion du carré Q17 - TCC Factorise le trinôme suivant:

#p2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m2</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m2</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>m1</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m1</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>m2</mi><mo>.</mo><mn>1</mn></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille de calculs</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.5 - Trinôme complétion du carré Q2 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

#p1

#p2





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Coefficients</mi><mo> </mo><mi>positifs</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q3 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Il faut préciser que plusieurs réponses sont parfois possibles lorsque le signe de certains coefficients numériques est négatif.

#p1

#p2





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>*</mo><mi>y</mi><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q4 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q5 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>sol</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q6 - DME Factorise le polynôme ci-dessous.

#p

]]> Le polynôme à factoriser comporte 4 termes.  La double mise en évidence sera probablement la méthode à utiliser.  Lorsque le signe de certains coefficients numériques est négatif, la factorisation peut prendre plus d'une forme.

Débutons par une première mise en évidence sur chaque paire de termes:

En factorisant les 2 premiers termes:#f1   ,on obtient: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

La factorisation des 2 derniers termes:#f2 nous donne: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math»

En complétant par la mise en évidence du facteur commun «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»21«/mn»«/mrow»«/mfenced»«/math», on obtient finalement:  

 #sol





]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>p</mi><mo>-</mo><mi>f2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><mi>y</mi><mo>+</mo><mn>32</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>→</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>facf2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.1 - Double mise en évidence Q7 - DC Factorise le polynôme ci-dessous.

#p1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>=</mo><mo>-</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>p11</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.2 - Différence de carrés Q8 - DC Factorise la différence de carrés suivante:

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.2 - Différence de carrés Q9 - DC Factorise le polynôme suivant:

#p

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mo>(</mo><msqrt><mi>a</mi></msqrt><mo>∉</mo><naturalnumbers/><mo>∨</mo><msqrt><mi>b</mi></msqrt><mo>∉</mo><naturalnumbers/><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>e</mi><mo>=</mo><mn>2</mn><mo>∧</mo><msqrt><mfenced close="&verbar;" open="&verbar;"><mi>b</mi></mfenced></msqrt><mo>∈</mo><naturalnumbers/></mrow><mrow><mi>b</mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>1</mn></mrow></apply></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>,</mo><integers/><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p</mi><mo>,</mo><integers/><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>-</mo><mi>b</mi><mo>)</mo></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.2.2 - Différence de carrés Trinôme ax^2+bx+c (copie) Factorise le trinôme suivant:

#p2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>gcd</mi><mo>(</mo><mi>m2</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m2</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mi>gcd</mi><mo>(</mo><mi>m1</mi><mo>.</mo><mn>0</mn><mo>,</mo><mi>m1</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>factor</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>m2</mi><mo>.</mo><mn>1</mn></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille de calculs</mtext></math></title><properties><property name="lang">fr</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1 - Devoirs sur l'algèbre/1.3 - Division de polynômes Division de polynômes_explication_gif[ID:pol_div_explication] ]]> 0.0000000 0.0000000 0 Q1 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math 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open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Le</mi><mo> </mo><mi>rest</mi><mo> </mo><mi>est</mi><mo> </mo><mn>0</mn><mo> </mo><mi>puisque</mi><mo> </mo><mi>i</mi><mo>=</mo><mn>0</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q10 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
 
 #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes avec reste Q11 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sans</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>i</mi><mo>=</mo><mn>0</mn></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>f</mi><mn>3</mn></msup><mo>+</mo><mi>g</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>f</mi><mn>2</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="digitgroupseparators">\s</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option><option name="digit_group_separator"></option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q2 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes avec reste Q3 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Sans</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>car</mi><mo> </mo><mi>i</mi><mo>=</mo><mn>0</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>e</mi><mo>=</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>-</mo><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mn>12</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q4 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes avec reste Q5 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ici</mi><mo> </mo><mi>sans</mi><mo> </mo><mi>reste</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q6 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

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#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>f</mi><mn>3</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="digitgroupseparators">\s</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes avec reste Q7 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sans</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>i</mi><mo>=</mo><mn>0</mn></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>+</mo><mi>e</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>g</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q8 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sans</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>i</mi><mo>=</mo><mn>0</mn></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>*</mo><msup><mi>f</mi><mn>3</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>f</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi><mo>=</mo><mi>quo_rem</mi><mo>(</mo><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi><mo>=</mo><mi>Rep</mi><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr1</mi><mo>=</mo><mi>d1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>p1</mi><mo>-</mo><mi>pr1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr2</mi><mo>=</mo><mi>d2</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>pr2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes sans reste Q9 - Division de polynômes Effectue la division de polynômes suivante.  Si la division s'effectue sans reste, écrire 0  pour le reste.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨22px¨»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#247;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]>
#p1
   #p2                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/math»    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«mo»+«/mo»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#191919¨»#«/mo»«mi mathcolor=¨#191919¨»s«/mi»«mn mathcolor=¨#191919¨»2«/mn»«mo mathcolor=¨#E5C304¨»#«/mo»«mi mathcolor=¨#E5C304¨»d«/mi»«mi mathcolor=¨#E5C304¨»d«/mi»«mn mathcolor=¨#E5C304¨»3«/mn»«/math»  Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF00FF¨»#«/mo»«mi mathcolor=¨#FF00FF¨»d«/mi»«mn mathcolor=¨#FF00FF¨»1«/mn»«/math» nous devons faire la division de #t1 par #t2  #r1      Ensuite il faut effectuer le produit de #d1 par #p2.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«mi»r«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/math»      Ce résultat (#pr1) est soustrait de #p1  #r2      Nous procédons de la même façon avec  #r1 qui est le reste de la soustraction #s1#ppr3
     Pour déterminer «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#00FF00¨»#«/mo»«mi mathcolor=¨#00FF00¨»d«/mi»«mn mathcolor=¨#00FF00¨»2«/mn»«/math» nous devons faire la division de #t3 par #t2   #r3                            
Pour revoir la procédure complète, clique ici
]]> 1.0000000 0.3333333 0 0 Quotient=#solReste=#reste]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pas</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>max1</mi><mo>.</mo><mo>.</mo><mi>pas</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Avec</mi><mo> </mo><mi>reste</mi><mo> </mo><mi>une</mi><mo> </mo><mi>fois</mi><mo> </mo><mi>sur</mi><mo> </mo><mi>deux</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>e</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>s</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>degree</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>&ges;</mo><mi>degree</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mi>leading_term</mi><mo>(</mo><mi>r2</mi><mo>)</mo><mo>/</mo><mi>leading_term</mi><mo>(</mo><mi>p2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>pr3</mi><mo>=</mo><mi>dd3</mi><mo>*</mo><mi>p2</mi></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>(</mo><mi>pr3</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>pr3</mi></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>dd3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>ppr3</mi><mo>=</mo><mo>&quot;</mo><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>60</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>reste</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Rep</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>u</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="digitgroupseparators">\s</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option><option name="digit_group_separator"></option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">90 10</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.3 - Division de polynômes avec reste $course$/top/CSSBE/Sec 4/Algèbre/1 - Devoirs sur l'algèbre/1.4 - Opération sur les fractions rationnelles Q1 - Restrictions Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}

Troisième restriction : {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi><mo>=</mo><mi>n</mi><mo>*</mo><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>f</mi></msup><mo>*</mo><msup><mi>z</mi><mi>h</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi><mo>=</mo><mi>m</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>g</mi></msup><mo>*</mo><msup><mi>z</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>y</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>z</mi><mo>≠</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>*</mo><msup><mi>z</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mi>i</mi></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.1 - Simplifications et restrictions sur les fr Q2 - Restrictions Quelle est la restriction de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

Restriction : {#1}

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»#e

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>-</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mi>e</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mn>19</mn><mn>4</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.1 - Simplifications et restrictions sur les fr Q3 - Restrictions Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}



]]> Première resptriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.1 - Simplifications et restrictions sur les fr Question 13 : restrictions monôme/monôme Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}

Troisième restriction : {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi><mo>=</mo><mi>n</mi><mo>*</mo><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>f</mi></msup><mo>*</mo><msup><mi>z</mi><mi>h</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi><mo>=</mo><mi>m</mi><mo>*</mo><msup><mi>x</mi><mi>e</mi></msup><mo>*</mo><msup><mi>y</mi><mi>g</mi></msup><mo>*</mo><msup><mi>z</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>y</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>z</mi><mo>≠</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>*</mo><msup><mi>z</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mi>i</mi></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 14 : restrictions binôme/binôme Quelle est la restriction de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

Restriction : {#1}

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»#e

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mo>-</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mi>e</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>44</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mn>19</mn><mn>4</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>50</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 15 : restrictions 2bin/2bin Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}



]]> Première resptriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>h</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 16 : restrictions multiplication Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}

Troisième restriction : {#3}

Quatrième restriction : {#4}




]]> Première resptriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

Troisième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

#r3

Quatrième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r4

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>h</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 16 : restrictions multiplication Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}

Troisième restriction : {#3}

Quatrième restriction : {#4}




]]> Première resptriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

Troisième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

#r3

Quatrième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r4

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>h</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 17 : restrictions division Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Première restriction : {#1}

Deuxième restriction : {#2}

Troisième restriction : {#3}

Quatrième restriction : {#4}




]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»§#215;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«/math»

Première restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

Troisième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

#r3

Quatrième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r4

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>h</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 17 : restrictions division_Modifiée Donne toutes les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Note : Inscris seulement les valeurs. Sépare chacune d'elles par une virgule.

Les restrictions sont: {#1}





]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»§#215;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«/math»

Première restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

Troisième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«mo»§#8800;«/mo»«mn»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r5

Quatrième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

#r3

Cinquième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r4

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo><mo>≠</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>h</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>h</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>g</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>i</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>f</mi><mi>e</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>g</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mfrac><mi>d</mi><mi>c</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r5</mi><mo>=</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mi>h</mi><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>/</mo><mi>e</mi><mo>,</mo><mo>-</mo><mi>h</mi><mo>/</mo><mi>g</mi><mo>,</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>d</mi><mo>/</mo><mi>c</mi><mo>,</mo><mo>-</mo><mi>h</mi><mo>/</mo><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>19</mn><mo>,</mo><mo>-</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>11</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Question 17 : restrictions division_Modifiée Donne toutes les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»

Note : Inscris seulement les valeurs. Sépare chacune d'elles par une virgule.

Les restrictions sont: {#1}





]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»§#215;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«/math»

Première restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«mo»§#8800;«/mo»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»f«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«/mrow»«/mfrac»«/math»

#r1

Deuxième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«/mfrac»«/math»

#r2

Troisième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«mo»§#8800;«/mo»«mn»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r5

Quatrième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»6«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

#r3

Cinquième restriction

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«mo»§#8800;«/mo»«/mrow»«/math»0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow»«mi»x«/mi»«mo»§#8800;«/mo»«/mrow»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»

#r4

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>c</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>f</mi><mo>=</mo><mi>random</mi><mfenced close="]" 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>g</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mi>i</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>f</mi><mo>/</mo><mi>e</mi><mo>,</mo><mo>-</mo><mi>h</mi><mo>/</mo><mi>g</mi><mo>,</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>d</mi><mo>/</mo><mi>c</mi><mo>,</mo><mo>-</mo><mi>h</mi><mo>/</mo><mi>i</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>24</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>19</mn><mo>,</mo><mo>-</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>11</mn><mn>7</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>20</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mfrac><mn>9</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_restriction

Quelles sont les restrictions associées à l'addition suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent les polynômes situées au dénominateur de chacune des fractions.

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»ou«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«/math»   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol1 et #sol2

]]> #bad1 et #bad2

]]> #bad2 et #sol1

]]> #sol2 et #bad1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Division_restriction

Quelles sont les restrictions associées à la division suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent:

1- les polynômes situées au dénominateur de chacune des fractions 

2- ainsi qu'au numérateur de la fraction de droite puisqu'au lieu de diviser, on multiplie par l'inverse

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»,«/mo»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»et«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»3«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»f«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«mspace linebreak=¨newline¨/»«/math»  

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1 

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>r2</mi><mo>∪</mo><mi>r3</mi><mo>∪</mo><mi>r4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>R</mi><mo>.</mo><mi>i</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mfenced><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>Lb1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb1</mi><mo>,</mo><mi>R</mi><mo>.</mo><mi>i</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb1</mi><mo>,</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>Lb1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>Lb2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Q17 - Restrictions

Quelles sont les restrictions associées à la multiplication suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent les polynômes situées au dénominateur de chacune des fractions.

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»ou«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«/math»   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol1 et #sol2

]]> #bad1 et #bad2

]]> #bad2 et #sol1

]]> #sol2 et #bad1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.1 - Simplifications et restrictions sur les fr Q18 - Restrictions

Quelles sont les restrictions associées à la division suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent:

1- les polynômes situées au dénominateur de chacune des fractions 

2- ainsi qu'au numérateur de la fraction de droite puisqu'au lieu de diviser, on multiplie par l'inverse

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»,«/mo»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»et«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»3«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»f«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«mspace linebreak=¨newline¨/»«/math»  

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol

]]> #bad1 

]]> #bad2

]]> #bad3

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>r2</mi><mo>∪</mo><mi>r3</mi><mo>∪</mo><mi>r4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>R</mi><mo>.</mo><mi>i</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mfenced><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mi>Lb1</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb1</mi><mo>,</mo><mi>R</mi><mo>.</mo><mi>i</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Lb2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>Lb1</mi><mo>,</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>Lb1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi><mo>=</mo><mi>Lb2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.1 - Simplifications et restrictions sur les fr Q4 - Addition Sachant que les dénominateurs sont différents de zéro, quelle expression algébrique est équivalente à l'expression algébrique ci-dessous?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»-«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»m«/mi»«mo»-«/mo»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mo»#«/mo»«mi»f«/mi»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> 4.0000000 0.3333333 0 true true none Your answer is correct. Your answer is partially correct. Your answer is incorrect.
 
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»g«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»h«/mi»«/mrow»«/mfrac»«/math»
 
 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»k«/mi»«/mrow»«mrow»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfrac»«/math»
 
 

]]> MathML must be formed by a <math> element, not <IMG>MathML must be formed by a <math> element, not <IMG>Error parsing MathML: error on line 1 at column 1: Document is emptyError parsing MathML: error on line 1 at column 1: Document is empty
 
 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>a</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>b</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>-</mo><mn>2</mn><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mfenced><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>c</mi></mrow></mfenced><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>i</mi><mo>+</mo><mi>j</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>49</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>34</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>101</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>76</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Addition de fractions rationnelles (1)

Sachant que les dénominateurs sont différents 0, quelle expression algébrique réduite est équivalente à l'expression algébrique ci-dessous?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«/math»


]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»+«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mo»#«/mo»«mi»d«/mi»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mspace linebreak=¨newline¨/»«mfrac»«mstyle displaystyle=¨true¨»«mn»3«/mn»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mfrac»«mn»3«/mn»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 0 3#c]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>3</mn><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mrow><mo>#</mo><mi>c</mi></mrow></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator"></option><option name="implicit_times_operator">true</option><option name="imaginary_unit"></option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_fract_rationnelles_plus complexe-2(avec restrictions) Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>11</mn></mrow><mrow><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>30</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>72</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>56</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_fractions_rationnelles_plus complexe Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_plus complexe Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow><mrow><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_plus complexe-2 Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>33</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>22</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>54</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>90</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>42</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_plus complexe-2(avec restrictions) (copie) Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» tu peux seulement écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> Réponse simplifiée=#solRestrictions=#restr2]]> Réponse simplifiée= #solRestrictions= #restr3]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mn>2</mn></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mn>3</mn><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic" correctAnswer="2"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_plus complexe-2avec_dénominateurs_tjrs_différentss Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mtd></mtr><mtr><mtd><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></mtd></mtr></mtable><mrow><mi>p2</mi><mo>≠</mo><mi>p4</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>21</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>49</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>106</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>56</mn></mrow><mrow><mn>30</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>146</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>192</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>72</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple_Restrictions Effectue l'addition demandée.  Ne pas oublié la ou les restrictions.(exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Restrictions= #restricRép=#sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mo>-</mo><mi>d</mi><mo>/</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mfenced><mi>s</mi></mfenced><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/><mi>R</mi><mi>é</mi><mi>p</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \s</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30 70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_simple-2 Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>64</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple-2_Fractions_rat_Restrictions Effectue l'addition demandée.  Ne pas oublié les restrictions. (exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Restrictions= #restricRép= #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mi>b</mi><mo>,</mo><mi>b</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>/</mo><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>25</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>125</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/><mi>R</mi><mi>é</mi><mi>p</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30-70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_simple-2_Restrictions Effectue l'addition demandée.  Ne pas oublié les restrictions. (exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse= #solRestrictions= #restric]]> Réponse=#solRestrictions=#restric2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mi>b</mi><mo>,</mo><mi>b</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>≠</mo><mo>-</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>≠</mo><mi>b</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>25</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>125</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30-70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Addition_simple[ID:fractrad1] Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple[ID:fractrad1] Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple[ID:fractrad1] Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Addition_simple[ID:fractrad1] Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Calcme_Addition_fract_rationnelles_plus complexe-2(avec restrictions) (copie) Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">,mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">true</property><property name="item_separator">,</property><property name="lang">en</property><property name="precision">4</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi 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mathvariant="normal">v</mi><mo>=</mo><mi>length</mi><mfenced><mi>restr1</mi></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">L</mi><mo>=</mo><mfenced open="{" close="}"><mrow/></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∅</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>for</mi><mo>&#xA0;</mo><mi>i</mi><mo>&#xA0;</mo><mi>in</mi><mo>&#xA0;</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi mathvariant="normal">v</mi><mo>&#xA0;</mo><mi>do</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">L</mi><mo>=</mo><mi>append</mi><mfenced><mrow><mi mathvariant="normal">L</mi><mo>,</mo><msub><mi>restr1</mi><mi>i</mi></msub></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close="}"><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi mathvariant="normal">L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 2</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p1</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p2</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p3</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p4</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">L</mi><mo>=</mo></math></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Division_plus complexe-2(avec restrictions) Effectue la division demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Division_plus complexe-3(avec restrictions et négatifs) Effectue la division demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math 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definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Multiplication_plus complexe-2(avec restrictions avec négatifs) Effectue la multiplication demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn><mtext xml:lang="en">variables</mtext></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Multiplication_plus complexe-2(avec restrictions) Effectue la multiplication demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Multiplication_plus complexe-2(avec restrictions) Effectue la multiplication demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Q10 - Soustraction Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» tu peux seulement écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> Réponse simplifiée=#solRestrictions=#restr2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mtable><mtr><mtd><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L2</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L2</mi><mo>,</mo><mi>x</mi><mo>≠</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr2</mi><mo>=</mo><mi>L2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>19</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>50</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>106</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>≠</mo><mo>-</mo><mn>5</mn><mo>,</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>≠</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Q11 - Multiplication Effectue la multiplication demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.3 - Multiplication d'expressions rationnelles Q12 - Multiplication Dans l'expression algébrique ci-dessous, les dénominateurs sont différents de 0. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfrac»«/math»

Quel monôme est équivalent à l'expression ci-dessus? 

]]> 4.0000000 0.3333333 0 0 #monôme]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»5«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»4«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»§#215;«/mo»«mfrac»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mi»§#244;«/mi»«mi»m«/mi»«mi»e«/mi»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/mstyle»«mstyle displaystyle=¨true¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mi»i«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfenced»«/mstyle»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mi»§#244;«/mi»«mi»m«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«/math»

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Je</mi><mo> </mo><mi>génère</mi><mo> </mo><mn>2</mn><mo> </mo><mi>binômes</mi><mo> </mo><mo>(</mo><mn>1</mn><mo> </mo><mi>et</mi><mo> </mo><mn>2</mn><mo>)</mo><mo> </mo><mi>de</mi><mo> </mo><mi>sorte</mi><mo> </mo><mi>que</mi><mo> </mo><mi>ce</mi><mo> </mo><mi>soit</mi><mo> </mo><mi>des</mi><mo> </mo><mi>conjugués</mi><mo> </mo><mi>et</mi><mo> </mo><mi>que</mi><mo> </mo><mi>le</mi><mo> </mo><mi>rapport</mi><mo> </mo><mi>b</mi><mo>/</mo><mi>a</mi><mo> </mo><mi>ne</mi><mo> </mo><mi>soit</mi><mo> </mo><mi>pas</mi><mo> </mo><mi>un</mi><mo> </mo><mi>entier</mi><mo>.</mo><mo> </mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>b</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>3</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>b</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>∉</mo><integers/></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Je</mi><mo> </mo><mi>génère</mi><mo> </mo><mi>deux</mi><mo> </mo><mi>binômes</mi><mo> </mo><mo>(</mo><mn>3</mn><mo> </mo><mi>et</mi><mo> </mo><mn>4</mn><mo>)</mo><mo> </mo><mi>de</mi><mo> </mo><mi>sorte</mi><mo> </mo><mi>que</mi><mo> </mo><mi>le</mi><mo> </mo><mi>produit</mi><mo> </mo><mi>soit</mi><mo> </mo><mi>un</mi><mo> </mo><mi>trinôme</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>c</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mo>-</mo><mi>b</mi><mo>∧</mo><mi>c</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>c</mi><mo>≠</mo><mi>d</mi><mo>∧</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>≠</mo><mi>b</mi><mo>∧</mo><mi>d</mi><mo>≠</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>monôme</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi><mo>=</mo><mo>(</mo><mi>bin1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>bin2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi><mo>=</mo><mi>monôme</mi><mo>*</mo><mi>bin1</mi><mo>*</mo><mi>bin3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri2</mi><mo>=</mo><mi>bin3</mi><mo>*</mo><mi>bin4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri3</mi><mo>=</mo><mi>bin2</mi><mo>*</mo><mi>bin4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>monôme</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bin5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>36</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>72</mn><mo>*</mo><mi>x</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mi>n</mi><mi>ô</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.3 - Multiplication d'expressions rationnelles Q13 - Multiplication Effectue la multiplication demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn><mtext xml:lang="en">variables</mtext></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>*</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>10</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>17</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_factorized"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.4.3 - Multiplication d'expressions rationnelles Q14 - Division Effectue la division demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>24</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></mrow><mrow><mn>15</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>43</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.4 - Division d'expressions rationnelles Q15 - Division Effectue la division demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>32</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.4.4 - Division d'expressions rationnelles Q16 - Division Effectue la division demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#247;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>min1</mi><mo>=</mo><mo>-</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>max1</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>min1</mi><mo>.</mo><mo>.</mo><mi>max1</mi></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p31</mi><mo>=</mo><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><msup><mfenced><mrow><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mrow></mfenced><mi>j</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>p1</mi><mo>/</mo><mi>p2</mi></mrow></mfenced><mo>/</mo><mfenced><mrow><mi>p3</mi><mo>/</mo><mi>p4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>p2</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p4</mi><mo>)</mo><mo>∪</mo><mi>roots</mi><mo>(</mo><mi>p3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>length</mi><mo>(</mo><mi>restr1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>in</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>v</mi></mrow><mrow><mi>L</mi><mo>=</mo><mi>append</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>restr1</mi><mo>.</mo><mi>i</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr</mi><mo>=</mo><mi>sort</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>22</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mn>20</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restr1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> 1.4.4 - Division d'expressions rationnelles Q5 - Addition Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Q6 - Addition Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>4</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>64</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Q7 - Addition Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>+</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>48</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>33</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>22</mn></mrow><mrow><mn>6</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>54</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>90</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>42</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Q8 - Soustraction Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>10</mn></mrow><mrow><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_common_denominator"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Q9 - Soustraction Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> 1.4.2 - Addition et soustraction d'expressions rat Question 13A : restrictions monôme/monôme

Quelles sont les restrictions de la division suivante? 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»m«/mi»«mi»o«/mi»«mi»n«/mi»«mn»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>repeat</mi><mo> </mo><mi>m</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>3</mn><mo>.</mo><mo>.</mo><mn>25</mn></mrow></mfenced><mo> </mo><mi>until</mi><mo> </mo><mi>gcd</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mi>d</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced close="]" open="["><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math 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close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>21</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>*</mo><msup><mi>z</mi><mn>6</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mon2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mi>i</mi></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>≠</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>≠</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mi>z</mi><mo>≠</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Restriction_une fraction rationnelle (copie) Quelle est la restriction de la fraction rationnelle suivante :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>sol1</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Soustraction_plus complexe-2(avec restrictions) Effectue l'addition demandée.  Ne pas oublier les restrictions. 

N.B. Si les restrictions sont «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8800;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mtext»et«/mtext»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8800;«/mo»«mn»3«/mn»«/math» tu peux seulement écrire: -2, 3

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Réponse simplifiée= #solRestrictions= #restr]]> Réponse simplifiée=#solRestrictions=#restr2]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mtd></mtr><mtr><mtd><mi>p21</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>p2</mi><mo>=</mo><mi>p21</mi><mo>*</mo><mi>p3</mi></mtd></mtr><mtr><mtd><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></mtd></mtr><mtr><mtd><mi>p41</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>g</mi></mtd></mtr><mtr><mtd><mi>p4</mi><mo>=</mo><mi>p41</mi><mo>*</mo><mi>p21</mi></mtd></mtr></mtable><mrow><mi>p2</mi><mo>≠</mo><mi>p4</mi></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>&#xE9;</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>é</mi><mi>p</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mi mathvariant="normal">i</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>f</mi><mi mathvariant="normal">i</mi><mi>é</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="float_format">,mg</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">80 20</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_simple_Restrictions Effectue l'addition demandée.  Ne pas oublié les restrictions. (exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Restrictions= #restricRép= #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mi>b</mi><mo>,</mo><mi>b</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>18</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30-70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_simple_Restrictions Effectue l'addition demandée.  Ne pas oublié la ou les restrictions.(exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Restrictions= #restricRép=#sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mo>-</mo><mi>d</mi><mo>/</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>16</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow><mrow><mn>15</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mfenced><mi>s</mi></mfenced><mo>=</mo><mo>&#xA0;</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/><mi>R</mi><mi>&#xE9;</mi><mi>p</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \s</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30 70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_simple_Restrictions (copie) Effectue la soustraction demandée.  Ne pas oublier les restrictions (exemple: pour «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math» les restrictions sont: -1,1).

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 Restrictions= #restricRép= #sol]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mi>b</mi><mo>,</mo><mi>b</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>18</mn></mrow><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>restric</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>c</mi><mspace linebreak="newline"/><mi>R</mi><mi>é</mi><mi>p</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="nobracketslist">true</param><param name="itemseparators">;, \n, \,, \s</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30-70</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data><data name="inputCompound">true</data></localData></question> Soustraction_simple-1 Effectue l'addition demandée.  Ne pas tenir compte des restrictions.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>p1</mi><mo>/</mo><mi>p2</mi><mo>-</mo><mi>p3</mi><mo>/</mo><mi>p4</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSSBE/Sec 4/Algèbre/1.4 - Opérations sur les fractions rationnelles/1.4.1 - Simplification et restrictions sur les fractions rationnelles Addition_restriction

Quelles sont les restrictions associées à l'addition suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent les polynômes situées au dénominateur de chacune des fractions.

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»ou«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«/math»   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol1 et #sol2

]]> #bad1 et #bad2

]]> #bad2 et #sol1

]]> #sol2 et #bad1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Multiplication_restriction

Quelles sont les restrictions associées à la multiplication suivante:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#215;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«/mrow»«/mfrac»«/math»

]]> Les restrictions correspondent aux valeurs de la variable "x" qui annulent les polynômes situées au dénominateur de chacune des fractions.

Il faut donc trouver les valeurs de "x" telles que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»2«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mtext mathcolor=¨#FF0000¨»ou«/mtext»«mo mathcolor=¨#FF0000¨»§#160;«/mo»«mo mathcolor=¨#FF0000¨»#«/mo»«mi mathcolor=¨#FF0000¨»p«/mi»«mn mathcolor=¨#FF0000¨»4«/mn»«mo mathcolor=¨#FF0000¨»=«/mo»«mn mathcolor=¨#FF0000¨»0«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«/math»   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtext»et«/mtext»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»p«/mi»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8660;«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»-«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#8660;«/mo»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #sol1 et #sol2

]]> #bad1 et #bad2

]]> #bad2 et #sol1

]]> #sol2 et #bad1

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mi>b</mi><mo>,</mo><mi>d</mi><mo>,</mo><mi>f</mi></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>e</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>f</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p1</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p2</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p3</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>p4</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r4</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi><mo>=</mo><mi>r1</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi><mo>=</mo><mi>r3</mi><mo>.</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>.</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bad2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Restriction_une fraction rationnelle Quelle est la restriction de la fraction rationnelle suivante :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mfenced close="]" open="["><mn>0</mn></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>2</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mn>1</mn></munderover><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><msup><mi>x</mi><mi>i</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>d1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>sol1</mi><mo>.</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="itemseparators">;, \n</param><param name="decimalseparators">., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">true</option><option name="imaginary_unit">i</option><option name="decimal_separator">,</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question>