Which expression is a linear factor of x ^6 + x - 66? x + 1 x + 2 x + 4 none of the above

None of the above

Step-by-step explanation:

We are given that an expression

We have to find which expression is a linear factor of given expression.

1.

Factor theorem: if x+a is factor of polynomial  P(x) then

P(a)=0=Remainder .

If p(a)=0 then x+a is a factor of p(x)

By factor theorem

Hence, x+1 is not  a linear factor of given expression.

2.

By factor theorem

Hence, x+2 is not a linear factor of given expression.

3.x+4

By factor theorem

Hence, x+4 is not a linear factor of given expression.

None of the above