Question

If you were to factor x^3 + 2x^2 - x - 2 into a linear factor, then the answer would be (x+2)(x+1)(x-1). But how do you get it?

Answer 1

Doing what I do, you plug numbers that divide -(-2) into the equation until you get 0. This gives you (x - factor) as a root. Assuming I got (x-1), you do long division: \[(x^3+2x^2-x-2)/(x-1) = (x^2+3x+2)\]
The quadratic is much easier to factorise. and gives x^3 + 2x^2 - x - 2=(x+2)(x+1)(x-1)