Question

Descompuneti in produs de factori primi:(x²+x)(x²+x-8)+12.

Answer 1

(x² + x)(x² + x - 8) + 12 = y (y - 8) + 12 = y² - 8y + 12 = y² - 2y - 6y + 12 =
Notam x² + x = y
= y (y - 2) - 6 (y - 2) = (y - 6) (y - 2) = (x² + x - 6) (x² + x - 2) =
= (x² + 3x - 2x - 6) (x² + 2x - x - 2) = [x (x + 3) - 2 (x + 3)] [x (x + 2) - (x + 2)] =
= (x - 2) (x + 3) (x - 1) (x + 2).