-
$A(x)=4x - (2 - x)(x + 3)$
Corrigé
\[\begin{aligned}
A(x)&=4x - (2-x)(x + 3)&
\\
&=4x - (2x + 6 - x^2 - 3x)&
\\
&=4x - 2x - 6 +x^2 + 3x&
\\
&=x^2 + 5x - 6.&\\
\end{aligned}\]
-
$B(x)=3(x-2)(2x+5)$
Corrigé
\[\begin{aligned}
B(x)&=3(x-2)(2x+5)&
\\
&=3(2x^2 + 5x - 4x - 10)&
\\
&=3(2x^2 + x - 10)&
\\
&=6x^2 + 3x - 30.&
\end{aligned}\]
-
$C(x)=5x - (x+1)(6x-2)$
Corrigé
\[\begin{aligned}
C(x)&=5x - (x+1)(6x-2)&
\\
&=5x - (6x^2 - 2x + 6x - 2)&
\\
&=5x - (6x^2 + 4x - 2)&
\\
&=5x -6x^2 - 4x + 2&
\\
&=-6x^2 + x + 2.&
\end{aligned}\]
-
$D(x)=x(x-1)(x+2)$
Corrigé
\[\begin{aligned}
D(x)&=x(x-1)(x+2)&
\\
&=x(x^2 + 2x - x - 2)&
\\
&=x(x^2 + x - 2)&
\\
&=x^3 + x^2 - 2x.&
\end{aligned}\]
-
$E(x)=(2x+3)(x^2-2x+4)$
Corrigé
\[\begin{aligned}
E(x)&=(2x+3)(x^2 - 2x + 4)&
\\
&=2x^3 - 4x^2 + 8x + 3x^2 - 6x + 12&
\\
&=2x^3 - x^2 + 2x + 12.&
\end{aligned}\]
-
$F(x)=(x-1)(x^2 + x + 1)$
Corrigé
\[\begin{aligned}
F(x)&=(x-1)(x^2 +x + 1)&
\\
&=x^3 + x^2 + x - x^2 -x - 1&
\\
&=x^3 - 1.&
\end{aligned}\]
-
$G(x)=2(x+3)(x-1) - (4-x)(2x+3)$
Corrigé
\[\begin{aligned}
G(x)&=2(x+3)(x-1) - (4 - x)(2x + 3)&
\\
&=2(x^2 - x +3x - 3) - (8x + 12 - 2x^2 - 3x)&
\\
&=2(x^2 + 2x - 3) - (-2x^2 + 5x + 12)&
\\
&=2x^2 + 4x - 6 + 2x^2 - 5x - 12&
\\
&=4x^2 -x - 18.&
\end{aligned}\]
-
$H(x)=(x+1)(x-2)(x+3)$
Corrigé
\[\begin{aligned}
H(x)&=(x+1)(x-2)(x+3)&
\\
&=(x+1)[x^2 + 3x - 2x - 6]&
\\
&=(x+1)(x^2 + x - 6)&
\\
&=x^3 + x^2 - 6x + x^2 + x - 6&
\\
&=x^3 + 2x^2 - 5x - 6.&
\end{aligned}\]