- The Factor Theorem itself: is a factor of if and only if .
- If the constant term in is , then in any factor of the form , . must be a factor of
So in part (a), you'll only need to try values of which are factors of (not forgetting to try negative numbers as well), to see whether . If my arithmetic is correct, none of them works, so there aren't any linear factors with integer coefficients.
By the same reasoning, in part (b), are the only possibilities. So try first. And, even when you have found the first factor, keep on trying with the quotient until you're sure there are no factors left. (Hint: do you know anything about Pascal's triangle or the Binomial Theorem?)