Bonjour j’ai un gros soucis en math j’aimerais de l’aide : A(x)=(2x+1)(2-3x)+(2x+1)(x-5) B(x)=(2x+1)(1-3x)-(2x+1)(x+5) C(x)=(2x+1)(5-3x)-2(5-3x)(x-5) D(x)=(2x+1

Réponse :

Explications étape par étape

Bonsoir

A(x)=(2x+1)(2-3x)+(2x+1)(x-5)

B(x)=(2x+1)(1-3x)-(2x+1)(x+5)

C(x)=(2x+1)(5-3x)-2(5-3x)(x-5)

D(x)=(2x+1/3)(5-3x)-3(5-3x)(x+5/3)

1.developper A(x),B(x),C(x)et D(x)

A(x)=(2x+1)(2-3x)+(2x+1)(x-5)

A(x) = 4x - 6x^2 + 2 - 3x + 2x^2 - 10x + x - 5

A(x) = -4x^2 - 8x - 3

B(x)=(2x+1)(1-3x)-(2x+1)(x+5)

B(x) = 2x - 6x^2 + 1 - 3x - (2x^2 + 10x + x + 5)

B(x) = -6x^2 - x + 1 - 2x^2 - 11x - 5

B(x) = -8x^2 - 12x - 4

C(x)=(2x+1)(5-3x)-2(5-3x)(x-5)

C(x) = 10x - 6x^2 + 5 - 3x - 2(5x - 25 - 3x^2 + 15x)

C(x) = -6x^2 + 7x + 5 - 10x + 50 + 6x^2 - 30x

C(x) = -33x + 55

D(x)=(2x+1/3)(5-3x)-3(5-3x)(x+5/3)

D(x) = 10x - 6x^2 + 5/3 - x - 3(5x + 25/3 - 3x^2 - 5x)

D(x) = -6x^2 + 9x + 5/3 - 15x - 25 + 9x^2 + 15x

D(x) = 3x^2 + 9x - 75/3 + 5/3

D(x) = 3x^2 + 9x - 70/3

2.Calculer les valeurs de A(x),B(x),C(x)et D(x) pour x=0

A(0) = -4 * 0^2 - 8 * 0 - 3 = -3

B(0) = -8 * 0^2 - 12 * 0 - 4 = -4

C(0) = -33 * 0 + 55 = 55

D(0) = 3 * 0^2 + 9 * 0 - 70/3 = -70/3

3.Factoriser A(x),B(x),C(x)et D(x)

A(x)=(2x+1)(2-3x)+(2x+1)(x-5)

A(x) = (2x + 1)(2 - 3x + x - 5)

A(x) = (2x + 1)(-2x - 3)

B(x)=(2x+1)(1-3x)-(2x+1)(x+5)

B(x) = (2x + 1)(1 - 3x - x - 5)

B(x) = (2x + 1)(-4x - 4)

B(x) = -4(2x + 1)(x + 1)

C(x)=(2x+1)(5-3x)-2(5-3x)(x-5)

C(x) = (5 - 3x)(2x + 1 - 2(x - 5))

C(x) = (5 - 3x)(2x + 1 - 2x + 10)

C(x) = (5 - 3x) * 11

C(x) = 11(5 - 3x)

D(x)=(2x+1/3)(5-3x)-3(5-3x)(x+5/3)

D(x) = (5 - 3x)(2x + 1/3 - 3(x + 5/3))

D(x) = (5 - 3x)(2x + 1/3 - 3x - 5)

D(x) = (5 - 3x)(-x - 14/3)

4.Resoudre les équations A(x)=0 et B(x)=0

A(x) = (2x + 1)(-2x - 3) = 0

2x + 1 = 0 ou -2x - 3 = 0

2x = -1 ou 2x = -3

x = -1/2 ou x = -3/2

B(x) = -4(2x + 1)(x + 1) = 0

2x + 1 = 0 ou x + 1 = 0

2x = -1 ou x = -1

x = -1/2 ou x = -1