Réponses

Meilleure réponse !
  • Omnes
  • Modérateur confirmé
2014-02-26T18:24:11+01:00
Salut,

Exercice 1.10 :

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

B(x) = (4x - 5)(7x-1) - (4x-5)(3x+4)
B(x) = (4x-5)[(7x-1) - (3x+4)]
B(x) = (4x-5)(7x - 1 - 3x - 4)
B(x) = (4x - 5)(4x - 5)

C(x) = (2x+5)(7x-3) + (2x+5)
C(x) = (2x+5)(7x-3) + (2x+5)*1
C(x) = (2x+5)(7x-3+1)
C(x) = (2x + 5)(7x-2)

D(x) = (-4x-6)(2x-1) + (2x-3)(8x-11)
D(x) = 2(2x-3)(2x-1) + (2x-3)(8x-11)
D(x) = (2x-3)[2(2x-1) + 8x - 11]
D(x) = (2x-3)(4x - 2 + 8x -11)
D(x) = (2x-3) (12x-13)

E(x) = (x-8)(5+3x) - (x-8)(7-x)
E(x) = (x-8)[5+3x - (7-x)]
E(x) = (x-8)(5+3x-7+x)
E(x) = (x-8)(-2+4x)
E(x) = 2(x-8)(2x-1)

Exercice 1.11 :

A(x) = (2x+3)² + (2x+3)(x+2)
A(x) = (2x+3)(2x+3) + (2x+3)(x+2)
A(x) = (2x+3)[2x+3 + x+2]
A(x) = (2x+3)(3x + 5 )

B(x) =(4x-5)(7x-1) + (4x-5)²
B(x) = (4x-5)(7x-1) + (4x-5)(4x-5)
B(x) = (4x-5)[7x-1+4x-5]
B(x) = (4x-5)(11x -6)

C(x) = (2x-1)² + (2x-1)(8x-11)
C(x) = (2x-1)(2x-1) + (2x-1)(8x-11)
C(x) = (2x-1)[(2x-1) + 8x - 11]
C(x) = (2x-1)(2x-1+8x-11)
C(x) = (2x -11)(10x -12)
C(x) = 2(2x-11)(5x-6)

D(x) = (2x+5)(7x-3) - (2x+5)²
D(x) = (2x + 5)(7x-3) - (2x+5)(2x+5)
D(x) = (2x+5)[7x-3 - (2x+5)]
D(x) = (2x+5)(7x-3-2x-5)
D(x) = (2x+5)(5x-8)

E(x) = (x-8)(5+3x) - (x-8)(7-x)
E(x) = (x-8)[5+3x - (7-x)]
E(x) = (x-8)(5+3x-7+x)
E(x) = (x-8)(-2 + 4x)
E(x) = 2(x-8)(2x-1)

Exercice 1.12

A(x) = x² - 1
A(x) = x² - 1²
A(x) = (x+1)(x-1)

B(x) = 4x² - 9
B(x) = (2x)² - 3²
B(x) = (2x+3)(2x-3)

C(x) = (3x+1)² - 25
C(x) = (3x+1)² - 5²
C(x) = (3x + 1 + 5)(3x+1-5)
C(x) = (3x+6)(3x-4)
C(x)  = 3(x+2)(3x-4)

D(x) = (4x-3)² - x²
D(x) = (4x-3 + x)(4x-3-x)
D(x) = (5x-3)(3x-3)
D(x) = 3(5x-3)(x-1)

E(x) = (2-5x)² - 9x²
E(x) = (2x-5)² - (3x)²
E(x) = (2x-5-3x)(2x-5+3x)
E(x) = (-x-5)(5x-5)
E(x) = -(x+5)(5x-5)
E(x) = -5(x+5)(x-1)

F(x) = (4x-5)² - (3x+2)²
F(x) = [4x-5 - (3x+2)][4x-5 + 3x + 2]
F(x) = (4x-5-3x-2)(7x-3)
F(x) = (x-7)(7x-3)

Exercice 1.13

A(x) = (x-3)² - 16
A(x) = (x-3)² - 4²
A(x) = (x-3+4)(x-3-4)
A(x) = (x+1)(x-7)

B(x) = (5x-1)² - 4
B(x) = (5x-1)² - 2²
B(x) = (5x-1 -2)(5x-1+2)
B(x) = (5x-3)(5x +1)

C(x) = (x+5)² - 7
C(x) = (x+5)² - racine(7)²
C(x) = (x+5 + racine(7))(x+5-racine(7))

D(x) = (x-7)² - 2
D(x) = (x-7)² - racine(2)²
D(x) = (x-7 - racine(2))(x-7+racine(2))

E(x) = (x-7)² + 3
E(x) = (x-7)² + racine(3)²
E(x) = (x-7 + racine(3))(x-7 - racine(3))

Je cherche pour les F des exos 10 et 11