Question

Factorise:

x⁴ – x³ – 8x + 8

Answer 1

Given expression: x⁴ – x³ – 8x + 8

⇒ x³(x – 1) – 8(x – 1)

⇒ (x – 1) (x³ – 8)

⇒ (x – 1) (x³ – 2³)

We know that,

a³ – b³ = (a – b) (a² + ab + b²)

Hence,

⇒ (x – 1) (x – 2) (x² + 2x + 4)