Question

factorise x^3-13x^2-32x-20

Answer 1

x³ + 13x² + 32x + 20
Let p(x) = x³ + 13x² + 32x + 20
Put x = –1 in p(x), we get
p(–1) = (–1)³ + 13(–1)² + 32(–1) + 20
= (–1) + 13 + (–32) + 20
= 33 – 33 = 0
Hence (x + 1) is a factor of p(x)
Now divide p(x) with (x + 1), we get x² + 12x + 20
∴ p(x) = (x + 1)(x² + 12x + 20)
Let's factorize x² + 12x + 20
⇒ p(x) = (x + 1)(x² + 10x + 2x + 20)
= (x + 1)[x(x + 10) + 2(x + 10)]
= (x + 1)(x + 10)(x + 2)