# Find The H C F ? If

The H C F of X^{8} – 1 and X^{4} + 2 X^{3} – 2 X – 1 is :

- X
^{2}+ 1 - X – 1
- X
^{2}– 1 - X + 1

**Answer: (3) X ^{2} – 1**

**Explanation:-**

X^{2} + 1

The factors of X^{8} – 1 = (X^{2})^{3} – (1)^{3}

= (X^{2} – 1) (X^{4} + 1 + 2 X^{2})

The factors of X^{4} + 2 X^{3} – 2 X – 1 = X^{4} – 1 + 2 X^{3} – 2 X

= (X^{2} – 1) (X^{2} + 1 ) + 2 X (X^{2} – 1)

= (X^{2} – 1) (X^{2} + 1 + 2 X)

H C F = (X^{2} – 1)

Then, the H C F of X^{8} – 1 and X^{4} + 2 X^{3} – 2 X – 1 is X^{2} – 1.

Hence, the answer is X^{2} – 1.