Factoriser : b- f(x) = x² + 4x +4 -(x+2) c- f(x) = (x+1)(x+3) - x - 1 d- f(x) = (x+5)² - (2x-7)² e- f(x)= -4x² + 4x - 1 Help ..

Factoriser revient à écrire sous forme simplifiée, en trouvant le facteur commun.

b- f(x)=x²+4x+4-(x+2)

f(x)=(x+2)²-(x+2)               Facteur commun :(x+2)

f(x)=(x+2)(x+2+1)

f(x)=(x+2)(x+3)

c- f(x)=(x+1)(x+3)-x-1

f(x)=x²+3x+x+3-x-1

f(x)=x²+3x+2

f(x)=(x+3/2)²-1/4

f(x)=(x+3/2)²-(1/2)²             forme(a²-b²)

f(x)=(x+3/2-1/2)(x+3/2+1/2)

f(x)=(x+1)(x+2)

d f(x)=(x+5)²-(2x-7)²       a²-b²=(a-b)(a+b)

f(x)=(x+5-2x+7)(x+5+2x-7)

f(x)=(12-x)(3x-2)

e - f(x)=-4x²+4x-1

f(x)=-(2x+2)²-5

b)

x^2+4x+4-(x+2)=(x+2)(x+2)+4-(x+2)=(x+2)(x+2+4-1)=(x+2)(x+5)

c)

(x+1)(x+3) - x - 1=(x+1)(x+3) - (x + 1)=(x+1)(x+3-1)=(x+1)(x+2)

d)

(x+5)² - (2x-7)²=((x+5)-(2x-7))((x+5)+(2x-7))=(-x+12)(3x-2)=(12-x)(3x-2)

e)

-4x² + 4x - 1=-1(4x² - 4x + 1)=-1(2x-1)(2x-1)

bonne chance