Réponse:
G= 4x² +12x +9
G= (2x)² + 2×2x×3 +3²
G= (2x+3)²
H= 9x² +25 -30x
H= 9x² -30x +25
H= (3x)² - 2×3x×5 +5²
H= (3x -5)²
I= (x+3)² -16
I= (x+3)² -4²
I= (x+3-4)(x+3+4)
I= (x-1)(x+7)
J= (x+1)² -(-3x+1)²
J= (x+1-(-3x+1))×(x+1+(-3x+1))
J= (x+1+3x-1)×(x+1-3x+1)
J= (x+3x)×(x-3x+1+1)
J= 4x × (-2x+2)
J= 4x × (-2(x -1)). Factoriser (-2x+2).
J= -4x ×2(x-1)
J= -4 ×2x(x-1)
J= -8x(x-1)
K= 81-(2x-7)²
K= 9² -(2x-7)²
K= (9-(2x-7)) × (9+(2x-7))
K= (9-2x+7)(9+2x-7)
K= (16-2x)(2+2x)
K= 2(8-x) × 2(1+x)
K= 2×2×(8-x)(1+x)
K= 4×(8-x)(1+x)
Exercice 4:
1) (3x-6)(5x-7)=0
3x-6 =0
3x = 6
3x/3 = 6/3
x = 2
5x-7 =0
5x = 7
5x/5 = 7/5
x = 7/5
L'équation a deux solutions : 2 ou 7/5
2) 3x(-2x-7) = 0
3x = 0
3x/3 = 0/3
x = 0
-2x-7 =0
-2x = 7
-2x/-2 = 7/-2
x = -7/2
L'équation a deux solutions : 0 ou -7/2
3) (7x-3)(2x+3) = 0
7x-3 = 0
7x = 3
7x/7 = 3/7
x = 3/7
2x+3 = 0
2x = -3
2x/2 = -3/2
x = -3/2
