Factorise: x^{3} + 13x^{2} + 32x + 20.

Let p(x) = x^{3} + 13x^{2} + 32x + 20

p(-1) = -1 + 13 - 32 + 20 = -33 + 33 = 0

Therefore (x + 1) is a factor of p(x).

On dividing p(x) by (x + 1) we get

p(x) (x + 1) = x^{2} + 12x + 20

Thus,

x^{3} + 13x^{2} + 32x + 20 = (x + 1)(x2 + 12x + 20)

= (x + 1) (x^{2} + 10x + 2x + 20)

= (x + 1)[x(x + 10) + 2(x + 10)]

= (x + 1) (x +2) (x + 10)

Hence, x^{3} + 13x^{2} + 32x + 20 = (x + 1) (x +2) (x + 10).