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f(x) = (3x - 1)^2 - x^2

a) developper :

f(x) = 9x^2 - 6x + 1 - x^2

f(x) = 8x^2 - 6x + 1

b) factoriser :

f(x) = (3x - 1 - x)(3x - 1 + x)

f(x) = (2x - 1)(4x - 1)

c) résoudre f(x) = 0 :

2x - 1 = 0 ou 4x - 1 = 0

2x = 1 ou 4x = 1

x = 1/2 ou x = 1/4

2) g(x) = (2x + 3)^2 - (2x + 3)(x - 1)

a) developper :

g(x) = 4x^2 + 12x + 9 - (2x^2 - 2x + 3x - 3)

g(x) = 4x^2 - 2x^2 + 12x + 2x - 3x + 9 + 3

g(x) = 2x^2 + 11x + 12

b) factoriser :

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

g(x) = (2x + 3)(x + 4)

c) Résoudre g(x) = 0

2x + 3 = 0 ou x + 4 = 0

2x = -3 ou x = -4

x = -3/2 ou x = -4

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

a) developper :

h(x) = 2x^2 - 2x + x - 1 + 6x^2 - 6x - 2x + 2

h(x) = 8x^2 - 9x + 1

b) factoriser :

h(x) = (2x + 1)(x - 1) + (3x - 1) * 2(x - 1)

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

h(x) = (x - 1)(2x + 1 + 6x - 2)

h(x) = (x - 1)(8x - 1)

c) résoudre h(x) = 0 :

x - 1 = 0 ou 8x - 1 = 0

x = 1 ou 8x = 1

x = 1 ou x = 1/8