x3 + 13x2 + 32x + 20
Let p(x) = x3 + 13x2 + 32x + 20
By trial, we find that
p(- 1) = (- 1)3 + 13(- 1)2 + 32(- 1) + 20
= - 1 + 13 - 32 + 20 = 0
∴ By Factor Theorem, x - (- 1), i.e., (x + 1) is a factor of p(x).
Now,
x3 + 13x2 + 32x + 20
= x2(x + 1) + 12x(x + 1) + 20(x + 1)
= (x + 1)(x2+ 12x + 20)
= (x + 1)(x2 + 2x + 10x + 20)
= (x + 1) {x(x + 2) + 10(x + 2)}
= (x + 1)(x + 2)(x + 10).