Question

What is the complete factorization of the polynomial below?
x^3 +4x^2 -x-4

Answer 1

(x + 1)(x - 1)(x + 4)

Explanation:

Group the polynomial:

(
`x^(3) + 4x^(2)`)(-x - 4)

Take out the GCF (Greatest Common Factor) for both:

`x^2` (x + 4) -1 (x + 4)

Put it together:

(
`x^2\\` - 1) (x + 4)

But, (
`x^2` - 1 ) can still be factored, by splitting it into 2:

(x + 1) (x - 1)

Now put it all together:

(x + 1)(x - 1)(x + 4)