Exercice 8 On note Z(x) = 3x+6+(x+2) (x-8) 1a) factoriser 3x +6 1b) Endéduire une factorisation de Z(x) 2) Factoriser a) w(x) = x² - 4(x-1) (x+2) b) H (x) = x²

1) Factoriser 3x+6 :
[tex]3x+6 \\ = 3x+2\times3 \\\\\boxed{=3(x+2)}[/tex]

Factoriser 3x+6+(x+2)(x-8) :
[tex]3x+6+(x+2)(x-8) \\ =3(x+2)+(x+2)(x-8) \\=(x+2)(3+x-8) \\\\\boxed{=(x+2)(x-5)}[/tex]

Factoriser w(x) : [tex]w(x) = x^{2} - 4(x-1) (x+2) \\ w(x)=x^{2}-2^{2}-4(x-1)(x+2) \\w(x)=(x+2)(x-2)-4(x-1)(x+2) \\ w(x)=(x+2)(x-2-4(x-1)) \\ w(x)=(x+2)(x-2-(4x-4)) \\ w(x)=(x+2)(x-2-4x+4) \\\\\boxed{w(x)=(x+2)(-3x+2)}[/tex]

Factoriser h(x) :
[tex]h(x) = x^{2}+4x +(x+1) (x+4) \\ h(x)=x(x+4)+(x+1)(x+4) \\ h(x)=(x+4)(x+x+1) \\\\\boxed{h(x)=(x+4)(2x+1)}[/tex]