retour
Factoriser les expressions suivantes.
-
$A(x) = (x-2)^2 - 36$.
Corrigé
\[\begin{aligned}
A(x)&=(x-2)^2 - 36&
\\
&=(x-2)^2 - 6^2&
\\
&=\left[(x-2) - 6\right]\left[(x-2) + 6\right]&
\\
&=(x-2-6)(x-2+8)&
\\
&=(x-8)(x+4)&
\end{aligned}\]
-
$B(x) = 1 - (2x + 3)^2$.
Corrigé
\[\begin{aligned}
B(x)&=1 - (2x+3)^2&
\\
&=1^2 - (2x+3)^2&
\\
&=\left[1 - (2x+3)\right]\left[1 + (2x+3)\right]&
\\
&=(1 - 2x - 3)(1 + 2x + 3)&
\\
&=(-2-2x)(4+2x)&
\end{aligned}\]
-
$C(x) = (3x - 2)^2 - (x+3)^2$.
Corrigé
\[\begin{aligned}
C(x)&=(3x-2)^2 - (x+3)^2&
\\
&=\left[(3x-2) - (x-3)\right]\left[(3x-2) + (x+3)\right]&
\\
&=(3x - 2 - x - 3)(3x - 2 + x + 3)&
\\
&=(2x - 5)(4x + 1)&
\end{aligned}\]
-
$D(x) = (x+5)^2 - (2x-4)^2.$
Corrigé
\[\begin{aligned}
D(x)&=(x+5)^2 - (2x - 4)^2&
\\
&=\left[(x+5) - (2x-4)\right]\left[(x+5) + (2x - 4)\right]&
\\
&=(x + 5 - 2x + 4)(x + 5 + 2x - 4)&
\\
&=(-x + 9)(3x + 1).&
\end{aligned}\]
retour