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\begin{document}


\begin{center}\section*{\textcolor{red}{2\up{nde} : TD \no 13 (factorisations)}}\end{center}




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\subsection{}
Factoriser les expressions suivantes :

\begin{enumerate}[$A(x)=$]

\medskip

\item  $3x – 15$


\medskip

\item  $4x^2 – 7x$


\medskip

\item  $3x^3 – 5x^2 + 8x$


\medskip

\item  $3a^2 - 6a$


\medskip

\item  $3x^3 + 9x^2$


\medskip

\item  $x(x + 5) + x(3x – 2)$


\medskip

\item  $2\sqrt{x} + x\sqrt{x}$
\end{enumerate}


\columnbreak



\subsection{}
En utilisant les factorisations de l'exercice II, donner des valeurs possibles pour lesquelles :

\begin{enumerate}[a)]

\medskip

\item  $3x-15=0$


\medskip

\item  $4x^2 – 7x=0$

\medskip


\medskip

\item  $3x^2 - 6x=0$
\end{enumerate}


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\subsection{}
Factoriser les expressions suivantes :


\begin{enumerate}[$A(x)=$]


\medskip

\item  $7x^3-3x^2$

\bigskip


\medskip

\item  $(2x - 3)(24x - 3) + (2x - 3)(-22x + 5)$.

\noindent On peut remarquer que : $\underbrace{(2x - 3)}_a\underbrace{(24x - 3)}_b + \underbrace{(2x - 3)}_a\underbrace{(-22x + 5)}_c=ab+ac$ en posant $\begin{cases}a=\cdots\\b=\cdots\\c=\cdots\end{cases}$

\bigskip


\medskip

\item  $(x + 4)(x – 6) + (– 1 + x)(x – 6)$

\bigskip


\medskip

\item  $(3x – 1)^2 – (3x – 1) $

\bigskip


\medskip

\item   $(15x + 7)(3 - x) + (12x + 5)(15x + 7)$

\bigskip


\medskip

\item  $7x - 26)(11x + 8) + (7x - 26)(12x + 4)$

\bigskip


\medskip

\item  $(13t + 5)(-5t + 2) - (8t - 15)(13t + 5)$


\end{enumerate}


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