Question

Which expression is a linear factor of x6 +x-66?

X+1

X+2

X+4

none of the above

Answer 1

none of the above

Explanation:

Answer 2

Option D.

Explanation:

The given expression is

`x^6+x-66`

It is a polynomial.

(x-c) is a linear factor of polynomial p(x) if p(c)=0.

Substitute x=-1 in the given expression.

`(1)^6+(1)-66=-64\\eq 0`

It means (x+1) is not a linear factor of given expression.

Substitute x=-2 in the given expression.

`(-2)^6+(-2)-66=-4\\eq 0`

It means (x+2) is not a linear factor of given expression.

Substitute x=-4 in the given expression.

`(-4)^6+(-4)-66=4026\\eq 0`

It means (x+4) is not a linear factor of given expression.

None of the given options are a linear factor of given expression.

Therefore, the correct option is D.