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The HCF of x^(5) - 1 and x^(4) + 2x^(5) ...

The HCF of `x^(5) - 1` and `x^(4) + 2x^(5) - 2x - 1` is :

A

`x ^(-2) -1 `

B

`x ^(2) +1`

C

`x +1`

D

`x -1`

Text Solution

Verified by Experts

The correct Answer is:
A
`x ^(8) - 1 = (x ^(4)) ^(2) - 1 ^(2) = (x ^(4) - 1) `
`= (x ^(4) -1) (x ^(2) -1) (x ^(2) +1)`
`x ^(2) + 2x ^(3) - 2x +1 = (x ^(4) - 1) + 2x (x ^(2) -1)`
`= (x ^(2) -1) [ (x ^(2) +1) + 2x]`
`= (x ^(2) -1) (x ^(2) + 2x +1)`
`therefore `म .स . `= x ^(2) -1`
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