Question

The H.C.F. of (x³ + x² + x + 1) and (x⁴ – 1) is
1. (x² – 1) (x² + 1)
2. (x² + 1) (x + 1) (x³ + 1)
3. (x + 1) (x² + 1)
4. (x + 1) (x² – 1)

Answer 1

Correct Answer - Option 3 : (x + 1) (x² + 1)

Given:

The H.C.F. of (x3 + x2 + x + 1) and (x4 – 1) is

Calculation:

⇒  (x3 + x2 + x + 1) = x²(x + 1) + 1(x + 1)

⇒ (x + 1) (x² + 1)

⇒ x⁴ – 1 = (x² – 1) (x² + 1)

⇒ (x + 1) (x – 1) (x² + 1)

∴ Required HCF is (x + 1) (x2 + 1)