Q12
P(x) = (x² - 1²) (4x+1) + (x-1)²
= (x+1) (x-1) (4x+1) + (x-1) (x-1)
= (x-1) [(x+1) (4x+1) + (x-1)]
= (x-1) (4x² + 5x + 1 + x - 1)
= (x-1) (4x² + 4x)
= 4x (x-1) (x+1)
puisque a² - b² = (a+b) (a-b)
donc
(x² - 1) = (x² - 1)² = (x+1) (x-1)