# What does the remainder theorem mean?

If a polynomial $P \left(x\right)$ is divided by $x - n$, then the remainder is $P \left(n\right)$.
So, for example if $P \left(x\right) = 3 {x}^{4} - 7 {x}^{2} + 2 x - 8$ is divided by $x - 3$, the the remainder is $P \left(3\right)$.