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\title{Technique: Evaluer et reduire}
\tribe{Troisième}
\date{Novembre 2017}

\pagestyle{empty}


\begin{document}

\begin{exercise}
    Évaluer les expressions suivantes

    \begin{multicols}{3}
        \begin{enumerate}
            \item $- x - 5$ en $x = 6$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; - 6 - 5 \\ 
                        A &amp; = &amp; -6 - 5 \\ 
                        A &amp; = &amp; -11
                    \end{eqnarray*}
                \end{solution}


            \item $- x + 8$ en $x = 1$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; - 1 + 8 \\ 
                        A &amp; = &amp; -1 + 8 \\ 
                        A &amp; = &amp; 7
                    \end{eqnarray*}
                \end{solution}

            \item $- x + 8$ en $x = 3$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; - 3 + 8 \\ 
                        A &amp; = &amp; -3 + 8 \\ 
                        A &amp; = &amp; 5
                    \end{eqnarray*}
                \end{solution}



            \item $-10 x^{  2 } + x - 6$ en $x = 7$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -10 \times 7^{  2 } + 7 - 6 \\ 
                        A &amp; = &amp; -10 \times 49 + 7 - 6 \\ 
                        A &amp; = &amp; -490 + 7 - 6 \\ 
                        A &amp; = &amp; -483 - 6 \\ 
                        A &amp; = &amp; -489
                    \end{eqnarray*}
                \end{solution}

            \item $-10 x^{  2 } + x - 6$ en $x = -5$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -10 \times ( -5 )^{  2 } - 5 - 6 \\ 
                        A &amp; = &amp; -10 \times 25 - 5 - 6 \\ 
                        A &amp; = &amp; -250 - 5 - 6 \\ 
                        A &amp; = &amp; -255 - 6 \\ 
                        A &amp; = &amp; -261
                    \end{eqnarray*}
                \end{solution}


            \item $-10 x^{  2 } + x + 10$ en $x = 8$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -10 \times 8^{  2 } + 8 + 10 \\ 
                        A &amp; = &amp; -10 \times 64 + 8 + 10 \\ 
                        A &amp; = &amp; -640 + 8 + 10 \\ 
                        A &amp; = &amp; -632 + 10 \\ 
                        A &amp; = &amp; -622
                    \end{eqnarray*}
                \end{solution}


            \item $-7 x ( x - ( -7 ) )$ en $x = -10$

            \item $-7 x ( x - ( -7 ) )$ en $x = -10$


            \item $( 8 x + 7 ) ( -5 - 2 x )$ en $x = -2$
        \end{enumerate}
    \end{multicols}
\end{exercise}

\begin{exercise}
    Réduis les expressions suivantes

    \begin{multicols}{3}
        \begin{enumerate}

            \item A = $x + 1 + x - 4$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; x + 1 + x - 4 \\ 
                        A &amp; = &amp; x + x + 1 - 4 \\ 
                        A &amp; = &amp; ( 1 + 1 ) x + 1 - 4 \\ 
                        A &amp; = &amp; 2 x - 3
                    \end{eqnarray*}
                \end{solution}

            \item B = $x + 6 + 3 + x - 6$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; x + 6 + 3 + x - 6 \\ 
                        A &amp; = &amp; x + 9 + x - 6 \\ 
                        A &amp; = &amp; x + x + 9 - 6 \\ 
                        A &amp; = &amp; ( 1 + 1 ) x + 9 - 6 \\ 
                        A &amp; = &amp; 2 x + 3
                    \end{eqnarray*}
                \end{solution}

            \item C = $-3 x + 5 + 5 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -3 x + 5 + 5 x \\ 
                        A &amp; = &amp; -3 x + 5 x + 5 \\ 
                        A &amp; = &amp; ( -3 + 5 ) x + 5 \\ 
                        A &amp; = &amp; 2 x + 5
                    \end{eqnarray*}
                \end{solution}


            \item D = $-4 + 2 x - 10 - 10 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -4 + 2 x - 10 - 10 x \\ 
                        A &amp; = &amp; 2 x - 4 - 10 - 10 x \\ 
                        A &amp; = &amp; 2 x - 14 - 10 x \\ 
                        A &amp; = &amp; 2 x - 10 x - 14 \\ 
                        A &amp; = &amp; ( 2 - 10 ) x - 14 \\ 
                        A &amp; = &amp; -8 x - 14
                    \end{eqnarray*}
                \end{solution}

            \item E = $-1 - 8 + 8 x + 6 - 4 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -1 - 8 + 8 x + 6 - 4 x \\ 
                        A &amp; = &amp; -9 + 8 x + 6 - 4 x \\ 
                        A &amp; = &amp; 8 x - 9 + 6 - 4 x \\ 
                        A &amp; = &amp; 8 x - 3 - 4 x \\ 
                        A &amp; = &amp; 8 x - 4 x - 3 \\ 
                        A &amp; = &amp; ( 8 - 4 ) x - 3 \\ 
                        A &amp; = &amp; 4 x - 3
                    \end{eqnarray*}
                \end{solution}

            \item E = $x^{  2 } + 3 + 3 x + 3 - 10 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; x^{  2 } + 3 + 3 x + 3 - 10 x \\ 
                        A &amp; = &amp; x^{  2 } + 3 x + 3 + 3 - 10 x \\ 
                        A &amp; = &amp; x^{  2 } + 3 x + 6 - 10 x \\ 
                        A &amp; = &amp; x^{  2 } + 3 x - 10 x + 6 \\ 
                        A &amp; = &amp; x^{  2 } + ( 3 - 10 ) x + 6 \\ 
                        A &amp; = &amp; x^{  2 } - 7 x + 6
                    \end{eqnarray*}
                \end{solution}


            \item F = $-6 x^{  2 } + 9 - 2 x - 2 - 6 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -6 x^{  2 } + 9 - 2 x - 2 - 6 x \\ 
                        A &amp; = &amp; -6 x^{  2 } - 2 x + 9 - 2 - 6 x \\ 
                        A &amp; = &amp; -6 x^{  2 } - 2 x + 7 - 6 x \\ 
                        A &amp; = &amp; -6 x^{  2 } - 2 x - 6 x + 7 \\ 
                        A &amp; = &amp; -6 x^{  2 } + ( -2 - 6 ) x + 7 \\ 
                        A &amp; = &amp; -6 x^{  2 } - 8 x + 7
                    \end{eqnarray*}
                \end{solution}

            \item G = $3 x^{  2 } + 1 x^{  2 } - 9 x - 9 + 3 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; 3 x^{  2 } + 1 x^{  2 } - 9 x - 9 + 3 x \\ 
                        A &amp; = &amp; 3 x^{  2 } + x^{  2 } - 9 x - 9 + 3 x \\ 
                        A &amp; = &amp; ( 3 + 1 ) x^{  2 } - 9 x - 9 + 3 x \\ 
                        A &amp; = &amp; 4 x^{  2 } - 9 x - 9 + 3 x \\ 
                        A &amp; = &amp; 4 x^{  2 } - 9 x + 3 x - 9 \\ 
                        A &amp; = &amp; 4 x^{  2 } + ( -9 + 3 ) x - 9 \\ 
                        A &amp; = &amp; 4 x^{  2 } - 6 x - 9
                    \end{eqnarray*}
                \end{solution}

            \item G = $-2 x^{  2 } + 7 - 6 x - 6 x^{  2 } - 2 x$
                \begin{solution}
                    \begin{eqnarray*}
                        A &amp; = &amp; -2 x^{  2 } + 7 - 6 x - 6 x^{  2 } - 2 x \\ 
                        A &amp; = &amp; -2 x^{  2 } - 6 x + 7 - 6 x^{  2 } - 2 x \\ 
                        A &amp; = &amp; -2 x^{  2 } - 6 x^{  2 } - 6 x + 7 - 2 x \\ 
                        A &amp; = &amp; ( -2 - 6 ) x^{  2 } - 6 x + 7 - 2 x \\ 
                        A &amp; = &amp; -8 x^{  2 } - 6 x + 7 - 2 x \\ 
                        A &amp; = &amp; -8 x^{  2 } - 6 x - 2 x + 7 \\ 
                        A &amp; = &amp; -8 x^{  2 } + ( -6 - 2 ) x + 7 \\ 
                        A &amp; = &amp; -8 x^{  2 } - 8 x + 7
                    \end{eqnarray*}
                \end{solution}
        \end{enumerate}
    \end{multicols}
\end{exercise}

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\end{document}

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