# How do you factor x^3 +5x^2-9x-45?

Oct 9, 2015

$\left(x + 3\right) \left(x - 3\right) \left(x + 5\right)$

#### Explanation:

Note that $\left(- 9 x - 45\right) = \left(- 9\right) \textcolor{b l u e}{\left(x + 5\right)}$
and that $\left({x}^{3} + 5 {x}^{2}\right) = \left({x}^{2}\right) \textcolor{b l u e}{\left(x + 5\right)}$

We can write
${x}^{3} + 5 {x}^{2} - 9 x - 45$
$\textcolor{w h i t e}{\text{XXX}} = \left({x}^{2} - 9\right) \textcolor{b l u e}{\left(x + 5\right)}$

If we further note that $\left({x}^{2} - 9\right)$ is the difference of squares $\textcolor{g r e e n}{\left(x + 3\right)} \textcolor{b r o w n}{\left(x - 3\right)}$
we can expand this to
${x}^{3} + 5 x - 9 x - 45$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{g r e e n}{\left(x + 3\right)} \textcolor{b r o w n}{\left(x - 3\right)} \textcolor{b l u e}{\left(x + 5\right)}$