Bonjour, pouvez vous m'aider à faire mon exercice s'il vous plait merci d'avance 1) Développer A(x), B(x), C(x) et D(x) A(x) = (2x+1)(2-3x) + (2x+1)(x-5) B(x) =

Réponse :

Explications étape par étape

Bonsoir

1) Développer 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 + 5x + x + 5)

B(x) = -8x^2 - 7x - 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) = 9x - 6x^2 + 5/3 - 15x - 25 + 9x^2 + 15x

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

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

2)Calculer les valeurs de A(x), B(x), C(x) et D(x) pour:

a) x = 0 b) x = 1 c) x = -2 d) x = 1/2 e) x = -2/3

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

A(0) = 3

A(1) = -4 * 1 - 8 * 1 - 3 = -4 - 8 - 3 = -15

A(-2) = -4 * (-2)^2 - 8 * -2 - 3 = -16 + 16 - 3 = -3

Tu continues...

B(x) = -8x^2 - 7x - 4

B(0) = -4

B(1) = -8 * 1 - 7 * 1 - 4 = -8 - 7 - 4 = -19

Tu continues...

C(x) = - 3x + 25

C(0) = 25

C(1) = -3 * 1 + 25 = -3 + 25 = 22

Tu continues...

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

D(0) = -70/3

D(1) = 3 * 1 + 9 * 1 - 70/3 = 3 + 9 - 70/3 = 12 - 70/3 = 36/3 - 70/3 = -34/3

Tu continues...

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 - 15/3)

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

4) On note E(x)= A(x)+B(x) et F(x)= C(x)+D(x)

a) montrer que E(x)= -(2x+1)(6x+7)

E(x) = (2x + 1)(-2x - 3) -4(2x + 1)(x + 1)

E(x) = (2x + 1)(-2x - 3 - 4(x + 1))

E(x) = (2x + 1)(-2x - 3 - 4x - 4)

E(x) = (2x + 1)(-6x - 7)

E(x) = -(2x + 1)(6x + 7)

b) montrer que F(x)= (-x+19/3)(5-3x)

F(x) = 11(5 - 3x) + (5 - 3x)(-x - 14/3)

F(x) = (5 - 3x)(11 - x - 14/3)

F(x) = (5 - 3x)(-x + 33/3 - 14/3)

F(x) = (5 - 3x)(-x + 19/3)

5) Développer E(x) et F(x)

E(x) = -(2x + 1)(6x + 7)

E(x) = -(12x^2 + 14x + 6x + 7)

E(x) = -12x^2 - 20x - 7

F(x) = (5 - 3x)(-x + 19/3)

F(x) = -5x + 95/3 + 3x^2 - 19x

F(x) = 3x^2 - 24x + 95/3

6) Calculer les valeurs de E(x) et F(x) pour :

a) x = 0 b) x = 1 c)x= -3 d)x= 1/2 e)x= -2/5

E(0) = -7

Tu continues..

F(0) = 95/3

Tu continues...