Answer:
Option D.
Step-by-step explanation:
The given expression is
[tex]x^6+x-66[/tex]
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.
[tex](1)^6+(1)-66=-64\neq 0[/tex]
It means (x+1) is not a linear factor of given expression.
Substitute x=-2 in the given expression.
[tex](-2)^6+(-2)-66=-4\neq 0[/tex]
It means (x+2) is not a linear factor of given expression.
Substitute x=-4 in the given expression.
[tex](-4)^6+(-4)-66=4026\neq 0[/tex]
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.
