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