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

Options

A. `4 ( x^(4) - x^(2) + 1)`
B. ` x^(3) - x + 4 x^(2)`
C. ` x^(3) - x + 3 x ^(2)`
D. None of these

Answer

A

Explanation

Let p(x)` = 8 ( x^(5) - x^(3) + x)`
`= 4 xx 2 xx x ( x^(4) - x^(2) + 1)`
and q(x) ` = 28 ( x^(6) + 1)`
`= 7 xx 4 [ ( x^(2))^(3) + (1)^(3)]`
`= 4 xx 7 xx ( x^(2) +1) ( x^(4) - x^(2) +1)`
`:.` HCF of p(x) and q(x) ` = 4 ( x^(4) - x^(2) + 1 )`