Question

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

Answer 1

None of the above

Explanation:

We are given that an expression

`x^6+x-66`

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

1.
`x+1`

`x+1=0`

`x=-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

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

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

2.
`x+2`

`x=-2`

By factor theorem

`(-2)^6-2-66=64-2-66-4\\eq 0`

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

3.x+4

`x=-4`

By factor theorem

`(-4)^6-4-66=4096-4-66=4026\\eq`

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

Answer: None of the above

Answer 2

I dont think any of these are. I get a linear factor of (x-2)