Réponse :
Explications étape par étape
Bonjour
soit A(x) = 7(1-2x)(3x+5) - (2x-1)(x+3)
1) Développer
A(x) = 7(3x + 5 - 6x^2 - 10x) - (2x^2 + 6x - x - 3)
A(x) = 21x + 35 - 42x^2 - 70x - 2x^2 - 5x + 3
A(x) = -44x^2 - 54x + 38
2)Factoriser
A(x) = 7(1-2x)(3x+5) - (2x-1)(x+3)
A(x) = 7(1 - 2x)(3x + 5) + (-2x + 1)(x + 3)
A(x) = (1 - 2x)[7(3x + 5) + x + 3]
A(x) = (1 - 2x)(21x + 35 + x + 3)
A(x) = (1 - 2x)(22x + 38)
A(x) = 2(11x + 19)(1 - 2x)
3) Vérifier
A(x) = 22x + 38 - 44x^2 - 76x
A(x) = -44x^2 - 54x + 38
4) Calculer A(0) , A(1/2) et A (-4)
A(0) = -44 * 0 - 54 * 0 + 38 = 38
A(1/2) = -44 * (1/2)^2 - 54 * 1/2 + 38
A(1/2) = -44/4 - 54/2 + 38
A(1/2) = -11 - 27 + 38
A(1/2) = -38 + 38 = 0
A(-4) = -44 * (-4)^2 - 54 * (-4) + 38
A(-4) = -44 * 16 + 216 + 38
A(-4) = -704 + 254
A(-4) = -450
5) Résoudre A(x)=0
2(11x + 19)(1 - 2x) = 0
11x + 19 = 0 ou 1 - 2x = 0
11x = -19 ou 2x = 1
x = -19/11 ou x = 1/2
