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Factoriser les expressions suivantes :
\[A(x)=x^2 - 9\;;\]
Corrigé
\[\begin{aligned}
A(x)&=x^2 - 9&
\\
&= x^2 - 3^2&
\\
&= (x-3)(x+3).&
\end{aligned}\]
\[B(x) =x^2-10x+25\;;\]
Corrigé
\[\begin{aligned}
B(x)&=x^2 - 10x + 25&
\\
&= x^2 - 2 \times x \times 5 + 5^2&
\\
&= (x- 5)^2.&
\end{aligned}\]
\[C(x) =\dfrac{x^2}{81}-\dfrac{16}{25}\;;\]
Corrigé
\[\begin{aligned}
C(x)&=\frac{x^2}{81} - \frac{16}{81}&
\\
&= \left(\frac x 9\right)^2 - \left(\frac 4 9\right)^2&
\\
&=\left(\frac x 9 - \frac 4 9\right)\left(\frac x 9 + \frac 4 9\right).&
\end{aligned}\]
\[D(x) =x^3 - 16x\;;\]
Corrigé
\[\begin{aligned}
D(x)&=x^3 - 16x&
\\
&= x(x^2 - 16)&
\\
&= x(x-4)(x+4).&
\end{aligned}\]
\[E(x) =(3x-1)^2 - (5+2x)^2\;;\]
Corrigé
\[\begin{aligned}
E(x)&=(3x-1)^2 - (5+2x)^2&
\\
&= \left[(3x-1) - (5+2x)\right]\left[(3x-1)+(5+2x)\right]&
\\
&=[3x-1-5-2x][3x-1+5+2x]&
\\
&= (x-6)(5x+4).&
\end{aligned}\]
\[F(x) =(3x-1)x^2 - 49(3x-1).\]
Corrigé
\[\begin{aligned}
F(x) &= (3x-1)x^2 - 49(3x-1)&
\\
&= (3x-1)(x^2 - 49)&
\\
&= (3x-1)(x-7)(x+7).&
\end{aligned}\]
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