Question

I'm having a hard time factoring polynomials, especially 3rd degree.

-x^3+2x^2+4x-8

-x^3-5x^2+20x+12

I don't know how to begin. I thought long division, but what would I divide by?

Answer 1

First find one root by trial and error. Call it a. Then divide (x-a) into the cubic using long division to get a quadratic equation. Get the roots of that by the usual method.

For the equation
-x^3+2x^2+4x-8,
one of the roots is x=2. Divide (x-2) into -x^3+2x^2+4x-8, and you get
-x^2 + 4 = (4-2)(x+2)
That completes the factoring.

-x^3+2x^2+4x-8 = (x-2)(x+2)(2-x)