# How do you use the remainder theorem to see if the p-2 is a factor of p^4-8p^3+10p^2+2p+4?

Sep 28, 2016

The remainder = 0, which means that $\left(p - 2\right)$ is a factor of the expression.

#### Explanation:

Let $f \left(p\right) = {p}^{4} - 8 {p}^{3} + 10 {p}^{2} + 2 p + 4$

If $p - 2 = 0 \text{ } \rightarrow p = 2$

Find $f \left(2\right)$ which will give the remainder.

$f \left(2\right) = {2}^{4} - 8 {\left(2\right)}^{3} + 10 {\left(2\right)}^{2} + 2 \left(2\right) + 4$

$f \left(2\right) = 16 - 64 + 40 + 4 + 4 = 0$

The remainder = 0, which means that $\left(p - 2\right)$ is a factor of the expression.