Find the GCD of the following

x³ – x² + x – 1, x⁴ – 1

x³ – x² + x – 1, put x = 1

Then,1 – 1 + 1 – 1 = 0

Since, this equation is divisible by x – 1

(x – 1)(x² + 1) = (x + 1)(x² + 1)

In second equation,

x⁴ – 1 = (x²)² – 1 = (x² – 1)(x² + 1) = (x + 1)(x – 1)(x² + 1)

[using a² – b² = (a – b)(a + b)]

Greatest common divisor = (x + 1)(x² + 1)