Question

Is (x − 2) a factor of f(x) = x3 − 2x2 + 2x + 3? Use either the remainder theorem or the factor theorem to explain your reasoning.

Answer 1

We have $f(2)=2^3-2^3+2^2+3=7\neq0$, so by the remainder theorem $x-2$ is not a factor of $f(x)$. (The remainder would have been 0 if it were a factor.)