Réponse :
f(x) = (2x - 1)(x + 3) + (2x - 1)(x - 2)
1) f(x) = (2x² + 6x - x - 3) + (2x² - 4x - x + 2)
f(x) = 4x² - 1
2) 2x - 1 est le facteur commun
f(x) = (2x - 1)(x + 3 + x - 2)
f(x) = (2x - 1)(2x + 1)
3) a. f(0) = 4*0² - 1 = -1
b. f(x) = 0 donc (2x - 1)(2x + 1) = 0
On a 2x - 1 = 0 ou 2x + 1 = 0
2x = 1 ou 2x = -1
x = 1/2 ou x = -1/2
c. f(x) = -1 donc 4x² - 1 = -1
4x² = 0
x² = 0
x = 0
