Factorize

x³ + 13x² + 32x + 20

Let p(x) = x³ + 13x² + 32x + 20

By trial, we find that p(–1) = 0, so by Factor theorem,

(x + 1) is the factor of p(x)

When we divide p(x) by (x + 1), we get x² + 12x + 20.

Now, (x² + 12x + 20) is a quadratic and can be solved by splitting the middle terms.

We have x² + 12x + 20= x² + 10x + 2x + 20

⇒ x (x + 10) + 2 (x + 10)

⇒ (x + 2)(x + 10)

So, x³ + 13x² + 32x + 20 = (x + 1)(x + 2)(x + 10)