Question

How do you use the factor theorem to determine whether x+1/3 is a factor of `f(x) = 3x^4 + x^3 - 3x + 1`?

Answer 1

It is not a factor since `f(-1/3)!=0`
So it will leave a remainder when long divided in.

Explanation:

If `(x+1/3)` is a factor of `f(x)`, then when divided into f it must leave no remainder, ie. `f(-1/3)` must be zero.

But : `f(-1/3)=3(-1/3)^4+(-1/3)^3-3(-1/3)+1`

`=2`

`!=0`

`therefore (x+1/3)` is not a factor of `f(x)`.