Question

Factorise x3-7x-6
Plz give clear explanation

Answer 1

$x^3-7x-6\\=x^3+x^2-x^2-7x-6\\=x^3+x^2-(x^2+7x+6)\\=x^2(x+1)-(x^2+6x+x+6)\\=x^2(x+1)-[(x+6)(x+1)]\\=(x+1)[x^2-(x+6)]\\=(x+1)(x^2-x-6)\\=(x+1)(x^2-3x+2x-6)\\=(x+1)([x(x-3)+2(x-3)]\\=(x+1)(x+2)(x-3)$