Question

Factorise x^3+2x^2-x-2

Answer 1

Solution

$x {}^{3} + 2x {}^{2} - x - 2 \\ =x {}^{3} - x {}^{2} + 3x {}^{2} - 3x + 2x - 2 \\ = x {}^{2} (x - 1) + 3x(x - 1) + 2(x - 1) \\ = (x - 1)(x {}^{2} + 3x + 2) \\ = (x - 1)(x {}^{2} + 2x + x + 2) \\ = (x - 1)(x + 2)(x + 1)$