CORRECTION
POUR ALLER PLUS LOIN
Factoriser les expressions suivantes :
A(x) = 2 x – 32–6 x – 9x22 x – 3
= (2 x−3)2−3(2 x−3)+(2 x−3)×1
= (2 x−3)[(2 x−3)−3(x+2)+1]
= (2 x−3)(2 x−3−3 x−6+1)
= (2 x−3)(−x−8)
B(x) = 2 x – 84 x – 1– 3 x12x8x – 42 x – 3
= 2(x−4)(4 x−1)−3(x−4)+(x−4)(2 x−3)
= (x−4)[2(4 x−1)−3(x+8)+(2 x+3)]
= (x−4)(8 x−2−3 x−24+2 x−3)
= (x−4)(7 x−29)
C(x) = x2– 3 x4 x – 12 x – 6
= x(x−3)+(4 x−1)2(x−3)
= (x−3)[x+2(4 x−1)]
= (x−3)(x+8 x−2)
= (x−3)(9 x−2)
D(x) = 5 x – 1x – 410 x – 2– 3 x41 – 5 x
= (5 x−1)(x−4)+2(5 x−1)(−3 x+4)−1×(5 x−1)
= (5 x−1)[(x−4)+2(−3 x+4)−1]
= (5 x−1)(x−4−6 x+8−1)
= (5 x−1)(−5 x+3) E(x) = 4 x2– 16 x3x – 2
= (2 x−1)(2 x+1)+3(2 x+1)(x−2)
= (2 x+1)[(2 x−1)+3(x−2)]
= (2 x+1)(2 x−1+3 x−6)
= (2 x+1)(5 x−7) F(x) = x2– 6 x94x2– 9
= (x−3)2+4(x−3)(x+3)
= (x−3)[(x−3)+4(x+3)]
= (x−3)(x−3+4 x+12)
= (x−3)(5 x+9)
G(x) = x22 x1–2 x2– x7
= (x+1)2−2(x+1)(−x+7)
= (x+1)[(x+1)−2(−x+7)]
= (x+1)(x+1+2 x−14)
= (x+1)(3 x−13) H(x) = 2 x – 12–4 x32
= [(2 x−1)+(4 x+3)][(2 x−1)−(4 x+3)]
= (2 x−1+4 x+3)(2 x−1−4 x−3)
= (6 x+2)(−2 x−4)
I(x) = 2 x2– 4 x2x−14 x – 8
= 2(x2−2 x+1)+(x−1)(4 x−8)
= 2(x−1)2+(x−1)(4 x−8)
= (x−1)[2(x−1)+(4 x−8)]
= (x−1)(2 x−2+4 x−8)
= (x−1)(6 x−10)
J(x) = 4 x212 x9 – 16x – 12
= (2 x+3)2−(4(x−1))2
= [(2 x+3)−4(x−1)][(2 x+3)+4(x−1)]
= (2 x+3−4 x+4)(2 x+3+4 x−4)
= (−2 x+7)(6 x−1)