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2°/ Factoriser les expressions suivantes au maximum.
a) 9x² - 5x
d) 3x (4x-1)-(4x - 1)
b) (x + 1)(3x - 2) - 2x(x + 1)
c) (x-1)²-4
2°/ Factoriser les expressions suivantes au maximum.
a) 9x² - 5x
d) 3x (4x-1)-(4x - 1)
b) (x + 1)(3x - 2) - 2x(x + 1)
c) (x-1)²-4
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a) 9x² - 5x
= x ( 9x -5)
d) 3x (4x-1)-(4x - 1)
= (4x-1) ( 3x -1)
b) (x + 1)(3x - 2) - 2x(x + 1)
= (x+1) ( 3x-2 -2x)
= (x+1) ( x-2)
c) (x-1)²-4
4 = 2²
identité remarquable
a² - b² = (a-b)(a+b)
( x-1 -2) ( x-1 +2)
= (x-3) ( x+1)
Explications étape par étape:
a) x(9x - 5)
d) (4x -1) ( 3x - 1)
b) (x+ 1) ( 3x - 2 - 2x) = (x -1)(x -2)
c) = (x - 1)² - 2² = (x - 1 - 2)(x - 1 + 2) =( x - 3) (x + 1)