Factorize each of the following polynomials.

x³ + 13x² + 32x + 20

Given,

x³ + 13x² + 32x + 20,

put x = – 1

then, – 1 + 13 – 32 + 20 = 0

since, this equation is divisible by (x + 1).

according to the question,

x³ + 13x² + 32x + 20 = (x + 1)(x² + 12x + 20)

= (x + 1)[x² + 10x + 2x + 20]

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

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