# How do you factor 5x^3-45x?

May 9, 2016

$5 {x}^{3} - 45 x = 5 x \left(x - 3\right) \left(x + 3\right)$

#### Explanation:

To factor this expression, we must be able to factor each part of it. Then we look for common things, and pull them out. We can write our expression as a set of factors for each term as:

$\textcolor{b l u e}{5 {x}^{3}} - \textcolor{red}{45 x} = \textcolor{b l u e}{5 \cdot x \cdot x \cdot x} - \textcolor{red}{5 \cdot 3 \cdot 3 \cdot x}$

We can see that each term has a factor of $\textcolor{m a \ge n t a}{5}$ and $\textcolor{m a \ge n t a}{x}$ in common, so we can "pull those out"

$\textcolor{m a \ge n t a}{5 x} \left(\textcolor{b l u e}{x \cdot x} - \textcolor{red}{3 \cdot 3}\right)$

Finally, we can try to factor the expression further noticing that it is the difference of squares:

$5 {x}^{3} - 45 x = 5 x \left(x - 3\right) \left(x + 3\right)$