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\begin{center}\section*{\textcolor{red}{Correction des exercices de factorisation}}\end{center}

\subsection{}

\begin{enumerate}[$A=$]
\item $ 5\textcolor{red}{(x+1)}+x\textcolor{red}{(x+1)}=\boxed{\textcolor{red}{(x+1)(5+x)}}$

\item $\textcolor{red}{(x-1)}(2x+3)+\textcolor{red}{(x-1)}(5x-2)=(x-1)[(2x+3)+(5x-2)]=(x-1)(2x+3+5x-2)		=\boxed{\textcolor{red}{(x-1)(7x+1) }}$

\item  $\textcolor{red}{(2x -5)}(4x -3) -\textcolor{red}{(2x -5)}(3x -1)=(2x -5)[(4x -3) -(3x -1)]=(2x -5)(4x -3 -3x+1)	=\boxed{\textcolor{red}{(2x -5)(x -2) }}$						  

\item $2(3x -1)\textcolor{red}{(x+3)} -3\textcolor{red}{(x+3)}(4x+1)=(x+3)[2(3x -1) -3(4x+1)]=(x+3)(6x -2 -12x -3)=\boxed{\textcolor{red}{(x+3)( -6x -5)}}$\\
\textbf{\textcolor{blue}{Remarque}} : Attention à la gestion des signes dans le crochet   	    	    

\item $7\textcolor{red}{(x -7)} -x(x -7)+4\textcolor{red}{(x -7)}=(x -7)(7 -x+4)=\boxed{\textcolor{red}{(x -7)(11 -x) }}$

\item $\textcolor{red}{(2x+5)}(3x -7) -\textcolor{red}{(2x+5)}(5x -3)=(2x+5)[(3x -7) -(5x -3)]=(2x+5)(3x -7 -5x+3)=\boxed{\textcolor{red}{(2x+5)( -2x -4)}}$\\
On peut améliorer : $(2x+5)( -2x -4)=(2x+5)[ -2(x+2)]=\boxed{\textcolor{red}{ -2(2x+5)(x+2)}} $\\

\item $(5x+7)(x -1)+(x -1)(3x -4)=(x -1)[(5x+7)+(3x -4)]=(x -1)(5x+7+3x -4)=\boxed{\textcolor{red}{(x -1)(8x+3)}}$

\item $(3x -2)(x -5)+(x -5)2=(3x -2)(x -5)+(x -5)(x -5)=(x -5)[(3x -2)+(x -5)]=\boxed{\textcolor{red}{(x -5)(4x -7)}}$

\item $(x+7)(5x+2) -3(5x+2)2=(x+7)(5x+2) -3(5x+2)(5x+2)=(5x+2)[(x+7) -3(5x+2)]\\
=(5x+2)(x+7 -15x -6)=\boxed{\textcolor{red}{(5x+2)( -14x+1)}}$

\item $(3x -4)(2x+3) -(2x -3)(3x -4)=(3x -4)[(2x+3) -(2x -3)]=(3x -4)(2x+3 -2x+3)=(3x -4) (6)=\boxed{\textcolor{red}{6(3x -4)}}$
\end{enumerate}

\subsection{}

\begin{enumerate}[$A=$]

\item $(5x -2)+4(2x+1)(5x -2)=(5x -2)×1+4(2x+1)(5x -2)=(5x -2)[1+4(2x+1)]=(5x -2)(1+8x+4)\\
=\boxed{\textcolor{red}{(5x -2)(5+8x)}}$			

\item $7x(2x+3)+2x+3=7x(2x+3)+(2x+3) 1=\boxed{\textcolor{red}{(2x+3)(7x+1)}}$  	   								

\item $(3x+5)(x -1)+(x -1)=(3x+5)(x -1)+(x -1) 1=(x -1)[(3x+5)+1]=(x -1)(3x+5+1)	=\boxed{\textcolor{red}{(x -1)(3x+6)}}$ \textbf{\textcolor{blue}{(forme attendue)}}\\
$=(x -1)\times 3(x+2)=\boxed{\textcolor{red}{3(x -1)(x+2)}}$ \textbf{\textcolor{blue}{forme améliorée}} .   	   						  

\item $(7x -2)(3x+4) -(3x+4)	=(7x -2)(3x+4) -(3x+4) 1=(3x+4)[(7x -2) -1]=(3x+4)(7x -2 -1)\\
=\boxed{\textcolor{red}{(3x+4)(7x -3)}}$	
							
\item $(5x -1)(2x+3) -5x+1=(5x -1)(2x+3) -(5x -1)=(5x -1)(2x+3) -(5x -1) 1=(5x -1)[(2x+3) -1]\\
=(5x -1)(2x+3 -1)=\boxed{\textcolor{red}{(5x -1)(2x+2)}}$ \textcolor{blue}{(\textbf{forme attendue})}\\
$=\boxed{\textcolor{red}{2(5x -1)(x+1)}}$ \textcolor{blue}{(\textbf{forme améliorée})}    	   						  

\item $(7x -2)(x -9)+14x -4=(7x -2)(x -9)+2(7x -2)=(7x -2)[(x -9)+2]=(7x -2)(x -9+2)=\boxed{\textcolor{red}{(7x -2)(x -7) }}$	   								

\item $(x+4)2+(x -4)(x+4)+2x+8=(x+4)(x+4)+(x -4)(x+4)+2(x+4)=(x+4)[(x+4)+(x -4)+2]\\
=(x+4)(x+4+x -4+2)=\boxed{\textcolor{red}{(x+4)(2x+2)}}$ \textbf{\textcolor{blue}{(forme attendue)}}\\
$=\boxed{\textcolor{red}{2(x+4)(x+1)}}$\textbf{ \textcolor{blue}{(forme améliorée)  }}  	   						  

\item $(2x+6)(x -5)+3x+9=2(x+3)(x -5)+3(x+3)=(x+3)[2(x -5)+3]=(x+3)(2x -10+3)\\
=\boxed{\textcolor{red}{(x+3)(2x -7)}} $
\end{enumerate}

\label{fin}
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