# How do you use the factor theorem to determine whether x-3 is a factor of p(x)=x^3-4x^2+3x?

##### 1 Answer
Nov 29, 2015

The Factor Theorem says that
$\left(x - a\right)$ is a factor of $p \left(x\right)$ if and only if $p \left(a\right) = 0$

In this case, since $p \left(3\right) = 0$
$\textcolor{w h i t e}{\text{XXX}} \left(x - 3\right)$ is a factor of $p \left(x\right) = {x}^{3} - 4 {x}^{2} + 3 x$

#### Explanation:

$p \left(3\right) = {3}^{3} - 4 \cdot {3}^{2} + 3 \cdot 3 = 27 - 36 + 9 = 0$