`x^(6)-1` और `x^(4)+2x^(3)-2x^(1)-1` का म. स. क्या होगा।

Options

A. `x^(2)+1`
B. `x-1`
C. `x^(2)-1`
D. `x+1`

Answer

C

Explanation

`x^(6)-1implies (x^(2))^(3)-1^(3)`
Using
`implies a^(3)-b^(3)=(a-b)(a^(2)+b^(2)+ab)`
`implies(x^(2)-1)(x^(4)+1+x^(2)xx1)`
`implies (x^(2)-1)(x^(4)+1+x^(2))`………….i
Again
`x^(4)+2x^(3)-2x-1`
`implies x^(4)-1+2x(x^(2)-1)`
`implies (x^(2))^(2)-1^(2)+2x(x^(2)-1)`
`implies (x^(2)-1)(x^(2)+1)+2x(x^(2)-1)`
`implies (x^(2)-1)(x^(2)+1+2x)` ............ii
`implies` from equation i and ii
HCF is a common term
HCF `=(x^(2)-1)`