Réponse :
Bonjour
Explications étape par étape
a) x²-6x+9=(x-3)²
b) 2x-2+(x²-1)=2(x-1)+(x-1)(x+1)=(x-1)(2+x+1)=(x-1)(3+x)
c)5x^4-45x²=5x²(x²-9)=5x²(x-9)(x+9)
d) x^5+4x^4+4x^3 = x^3(x²+4x+4) =x^3(x+2)²
e) 25x²-4+(5x+2)(4x-7)= (5x)²-2²+(5x+2)(4x-7) =(5x-2)(5x+2)+(5x+2)(4x-7)
= (5x+2)(5x-2+4x-7)=(5x+2)(9x-9) = (5x + 2) * 9(x - 1) = 9(5x + 2)(x - 1)
f) (x+1)²+ x² - 1 = (x+1)(x+1)+(x-1)(x+1)=(x+1)(x+1+x-1)=(x+1)2x = 2x(x + 1)
g) (3x-6)(2x-1)-3(4-x²)=(3x-6)(2x-1)-3(2²-x²)
3(x-2)(2x-1)-3(2-x)(2+x)= 3(x - 2)(2x - 1) + 3(x - 2)(2 + x) = 3(x - 2)(2x - 1 + 2 + x) = 3(x - 2)(3x + 1)
