a) -3x + 4x² + 7x³
On considère que -1 est la racine évidente donc (x-(-1))(ax²+ bx+c) = (x+1) (ax²+ bx+c)
Donc -3x + 4x² + 7x³ = (x+1) (ax²+ bx+c)
-3x + 4x² + 7x³ = ax³ + bx² + cx + ax² +bx + c = ax³ +x²(a+b) + x(c+b) + c
Par identification:
a = 7
a + b =4
c + b = -3
7 + b = 4
b = 4 - 7 =
b = -3
c -3 = -3
c = 0
D'où -3x + 4x² + 7x³ = (x+1)(7x² + -3x) = x(x+1)(7x-3)
b) (x-1)(7x+5)+2(x-1)
(x-1)[(7x+5) + 2] = (x-1)(7x + 5 + 2) = (x-1)(7x + 7) = 7(x-1)(x+1)
c) (4x -1)(7x +3) + (x+3)(4x-1) = (4x -1)[(7x+3) + (x+3)] = (4x -1)(7x+3+x+3) = (4x-1)(8x+6) = 2(4x-1)(4x+3)
d) (-x + 1) (2x +1) - (2x +1) (x-10)
(2x +1)[(-x + 1) - (x-10)] = (2x +1)(-x + 1 -x + 10) = (2x +1)(-2x + 11) = -(2x - 11)(2x + 1)
