\documentclass[12pt,a4paper]{article}
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\begin{document}\pagestyle{empty}
	
\begin{center}CALCULATRICE TOL\'ER\'EE\end{center}\vskip -0cm
	

\boxit{4pt}{Minitest}\rightarrowfill\quad\boxit{3pt}{Corrigé}\vskip 0.3cm


$\bullet$ \hskip 1cm  \'Ecrire sous la forme canonique\vskip 1cm

$P(x) = x^2+6x+1 = {\red (x+3)^2-9+1 = (x+3)^2-8}$\vskip 1cm

$Q(x) = x^2-3x+7 = {\red (x-1,5)^2-1,5^2+7 = (x-1,5)^2+4,75}$\vskip 1cm

$R(x) = 2x^2-12x+8 = {\red 2\Big(x^2-6x+4\Big) = 2\Big((x-3)^2-9+4\Big) = 2\Big((x-3)^2-5\Big) = 2(x-3)^2+10}$\vskip 1cm


$\bullet$ \hskip 1cm  Factoriser les expressions suivantes\vskip 1cm

\begin{minipage}{0.45\linewidth}

$P(x) = x^2+4x+3  $

{\red \doublespacing
	
\hskip 1cm $=(x+2)^2-4+3 $

\hskip 1cm $=(x+2)^2-1 $

\hskip 1cm $=(x+2)^2-1^2$

\hskip 1cm $=(x+2-1)(x+2+1)$
	
\hskip 1cm $= (x+1)(x+3)$

}
\end{minipage}
\quad
\begin{minipage}{0.45\linewidth}
	
	$Q(x) = x^2-5x+4  $
	
	{\red \doublespacing
		
		\hskip 1cm $=(x-2,5)^2-2,5^2+4 $
		
		\hskip 1cm $=(x-2,5)^2-2,25 $
		
		\hskip 1cm $=(x-2,5)^2-1,5^2$
		
		\hskip 1cm $=(x-2,5-1,5)(x-2,5+1,5)$
		
		\hskip 1cm $=(x-4)(x-1)$
	}
\end{minipage}


\vskip 1cm


$R(x) = 3x^2-6x+3 = {\red 3\Big(x^2-2x+1\Big) = 3(x-1)^2}$\vskip 1cm

\newpage

\begin{center}CALCULATRICE TOL\'ER\'EE\end{center}\vskip -0cm

\boxit{4pt}{Minitest}\rightarrowfill\quad\boxit{3pt}{Corrigé}\vskip 0.3cm


$\bullet$ \hskip 1cm  \'Ecrire sous la forme canonique\vskip 1cm

$P(x) = x^2-6x+1 = {\red (x-3)^2-9+1 = (x-3)^2-8}$\vskip 1cm

$Q(x) = x^2+3x+7 = {\red (x+1,5)^2-1,5^2+7 = (x+1,5)^2+4,75}$\vskip 1cm

$R(x) = 5x^2-10x+25 = {\red 5\Big(x^2-2x+5\Big) = 5\Big((x-1)^2-1+5\Big) = 5\Big((x-1)^2+4\Big) = 5(x-1)^2+20}$\vskip 1cm


$\bullet$ \hskip 1cm  Factoriser les expressions suivantes\vskip 1cm

$P(x) = x^2-6x+5 = $\vskip 1cm

$Q(x) = x^2-5x+6 = $\vskip 1cm

$R(x) = 8x^2-16x+32 = $\vskip 1cm


\begin{minipage}{0.45\linewidth}
	
	$P(x) = x^2+4x+3  $
	
	{\red \doublespacing
		
		\hskip 1cm $=(x-3)^2-9+5 $
		
		\hskip 1cm $=(x-2)^2-4 $
		
		\hskip 1cm $=(x-3)^2-2^2$
		
		\hskip 1cm $=(x-3-2)(x-3+2)$
		
		\hskip 1cm $= (x-5)(x-1)$
		
	}
\end{minipage}
\quad
\begin{minipage}{0.45\linewidth}
	
	$Q(x) = x^2-5x+6  $
	
	{\red \doublespacing
		
		\hskip 1cm $=(x-2,5)^2-2,5^2+6 $
		
		\hskip 1cm $=(x-2,5)^2-0,25 $
		
		\hskip 1cm $=(x-2,5)^2-0,5^2$
		
		\hskip 1cm $=(x-2,5-0,5)(x-2,5+0,5)$
		
		\hskip 1cm $=(x-3)(x-2)$
	}
\end{minipage}


\vskip 1cm


$R(x) = 8x^2-16x+32 = {\red 8\Big(x^2-2x+4\Big) = 8\Big((x-1)^2+3\Big)}$\vskip 1cm


\end{document} 