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

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

Answer 2

Answer:

None of the above

Step-by-step 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

$(-1)^6-1-66=-66\neq 0$

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

2.$x+2$

$x=-2$

By factor theorem

$(-2)^6-2-66=64-2-66-4\neq 0$

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

3.x+4

$x=-4$

By factor theorem

$(-4)^6-4-66=4096-4-66=4026\neq$

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

Answer: None of the above