What is the HCF of 8(x^5 - x^3 + x) and 28(x^6 + 1)

What is the HCF of 8(x5 - x3 + x) and 28(x6 + 1)?

  1. (x4 + 1 - x2)
  2. 4(x4 + 1 - x2)
  3. 2(x4 + 1 - x2)
  4. None

Answer

28(x6 + 1) = 28(x2)3 + 13 = 7×4×(x2 + 1)(x4 + 1 - x2)

= 7(x2 + 1)×4(x4 + 1 - x2) 

Also, 8 (x5 - x3 + x) = 2x × 4(x4 + 1 - x2)

So, HCF = 4(x4 + 1 - x2)

The correct option is B.