95
a)3x²+12x+12
=3(x²+4x+4) produit remarquable
=3(x+2)²
b)5x²-30x+45
=5(x²-6x+9)
=5(x-3)²
c)4x²-24x+36
=(2x+6)²
d)-12x²+12x-3
=-(12x²-12x+3)
=-3(4x²-4x+1)
=-3(2x-1)²
100 b)
Factoriser 9x²-4
=(3x+2)(3x-2)
101
C=20x²-60x+45-(2x-3)(x+7)
1)Développer et réduire C
C=20x²-60x+45-(2x-3)(x+7)
=20x²-60x+45-(2x²+14x-3x-21)
=20x²-60x+45-2x²-14x+3x+21
=18x²-71x+66
2)Factoriser 20x²-60x+45
=5(4x²-12x+9)
=5(2x-3)²
3)En déduire une expression factorisée de C
C=20x²-60x+45-(2x-3)(x+7)
=5(2x-3)²-(2x-3)(x+7)
=5(2x-3)(2x-3)-(2x-3)(x+7)
=5(2x-3)(2x-3-x-7)
=5(2x-3)(x-10)
