Question

Factorise:

x³ + x² – 4x – 4

Answer 1

Let p(x) = x³ + x² – 4x – 4

Constant term of p(x) = – 4

Factors of – 4 are ±1, ±2, ±4

By trial, we find that p(–1) = 0, so (x + 1) is a factor of p(x)

Now, we see that x³ + x² – 4x – 4

= x²(x + 1) – 4(x + 1)

= (x + 1)(x² – 4)  ...[Taking (x + 1) common factor]

Now, x² – 4 = x² – 2²

= (x + 2)(x – 2)  ...[Using identity, a² – b² = (a – b)(a + b)]

∴ x³ + x² – 4x – 4 = (x + 1)(x – 2)(x + 2)