Exercice 6-Factoriser en utilisant les IR et un facteur commun Factoriser les expressions suivantes :
A = x² + 2x + 1+ (x + 1)(x + 3)
B = x² - 2x + 1 + 3x(x - 1)
C = 4x² - 16x +16-x(x-2)
D = 9x² + 36x + 36 - 2x(x + 2)
A = x² + 2x + 1+ (x + 1)(x + 3)
B = x² - 2x + 1 + 3x(x - 1)
C = 4x² - 16x +16-x(x-2)
D = 9x² + 36x + 36 - 2x(x + 2)
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Réponse :
bonjour!
Explications étape par étape :
A = x² + 2x + 1+ (x + 1)(x + 3)
=(x+1)² +(x+1)(x+3)
=(x+1) (x+1+x+3)
=(x+1) (2x+4)
B = x² - 2x + 1 + 3x(x - 1)
=(x-1)²+3x(x-1)
=(x-1) (x-1+3x)
=(x-1) (4x-1)
C = 4x² - 16x +16-x(x-2)
=[2(x-2)]² -x(x-2)
=(x-2) (2(x-2)-x)
=(x-2) (2x-4-x)
=(x-2) (x-4)
D = 9x² + 36x + 36 - 2x(x + 2)
=[3(x+2)]² - 2x(x+2)
=(x+2) (3(x+2)-2x)
=(x+2) (3x+6-2x)
=(x+2)(x+6)