2018-2019/PreStSauveur/1S/Flash/F_18_09_12-2.tex

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2018-09-13 09:51:07 +00:00
\documentclass[a4paper,12pt]{classPres}
\usepackage{tkz-fct}
\author{}
\title{}
\date{}
\begin{document}
\begin{frame}{Questions flashs}
Développer et réduire l'expression
\[ A = (x-3)\times4 - (x-3)^2\]
Mettre sous forme canonique
\[ B = 9x^2 - 54x + 65 \]
\textbf{Bonus} factoriser ces 2 expressions.
\end{frame}
\begin{frame}{Correction}
\begin{eqnarray*}
A &=& 4x - 12 - (x^2 - 6x +9) \\
&=& 4x - 12 - x^2 + 6x - 9 \\
&=& -x^2 + 10x - 21
\end{eqnarray*}
\hline
\begin{eqnarray*}
B = 9x^2 - 54x + 65
\end{eqnarray*}
\[ \alpha = \frac{-b}{2a} = 3 \]
\[ \beta = -\frac{b^2-4ac}{4a} = -\frac{36+38}{4} = -16 \]
\begin{eqnarray*}
B &=& 9(x - 3)^2 - 16 \\
\end{eqnarray*}
\end{frame}
\begin{frame}{Bonus}
\begin{eqnarray*}
A &=& (x-3)\times4 - (x-3)^2\\
&=& (x-3)(4 - x + 3)\\
&=& (x-3)(-x + 7)
\end{eqnarray*}
\hline
\begin{eqnarray*}
B &=& 9(x - 3)^2 - 16 \\
&=& \left[ 3(x-3) \right]^2- 4^2 \\
&=& ( 3x - 9 - 4 ) (3x - 9 + 4) \\
&=& (3x - 13)(3x - 5)
\end{eqnarray*}
\end{frame}
\end{document}