# How do you use the factor theorem to determine whether x-3 is a factor of  P(x) = x^3 - 2x^2 + 22?

$\left(x - 3\right)$ is not a factor.
If $\left(x - 3\right)$ is a factor, P(3) = 0. Here, P(3) = 31.
P(x) / (x-3) = ${x}^{2}$ + $\frac{22}{x - 2}$