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La forme factorisée est pratique pour résoudre des équations et étudier le signe de la fonction. \paragraph{Exemples}% -Relier les formes factorisées avec les formes développées +Relier les formes factorisées avec les formes développées qui sont égales +\medskip +\begin{minipage}{0.4\textwidth} + Formes développées + \begin{tabular}{@{}r@{\quad}>{$\bullet$}c@{}} + $4 x^3 - 20 x^2 + 28 x - 12$ &\\ + $3 x^2 - 3 x - 6$ &\\ + $-x^3 - x^2 + 4 x + 4$ &\\ + \end{tabular} +\end{minipage} +\begin{minipage}{0.4\textwidth} + Formes factorisées + + \begin{itemize} + \item $3(x+1)(x-2)$ + \item $-(x+1)(x-2)(x+2)$ + \item $4(x-3)(x-1)^2$ + \end{itemize} +\end{minipage} + +Vidéo sur la méthode pour faire de gros développement. \section{Étude de signe d'une forme factorisée} +\paragraph{Exemple} étude du signe de +\[ + f(x) = 3(2x-1)(-4x+1) +\] + +\section{Étude des variations d'un polynôme} + +\paragraph{Exemple} étude des variations de +\[ + f(x) = 0.1x^3 - 0.2x^2 - 0.4x + 10 +\] + \end{document}