Bonjour;
f(x) = x³ - 3x - 2 = x³ - x - 2x - 2 = x(x² - 1) - 2(x + 1)
= x(x - 1)(x + 1) - 2(x + 1) = (x² - x)(x + 1) - 2(x + 1)
= (x + 1)(x² - x - 2) = (x + 1)(x² - 2x + x - 2)
= (x + 1)(x(x - 2) + (x - 2)) = (x + 1)((x - 2)(x + 1))
= (x + 1)²(x - 2) .
Le tableau de variation est comme sur le fichier ci-joint .
