## Precalculus (10th Edition)

The Remainder Theorem says that the remainder when a function $f(x)$ is divided by $(x-r)$ is $f(r)$. Hence $f(2)=4\cdot8-3\cdot4-8\cdot2+4=8\ne0$, therefore $(x-2)$ is not a factor of $f(x)$ because of the Factor Theorem. The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and vice versa.