# How do you factor 9x^3-36x^2-25x+100?

Sep 1, 2016

$\left(x - 4\right) \left(3 x + 5\right) \left(3 x - 5\right)$

#### Explanation:

There are 4 terms, but there is no common factor in all the terms,
Pair the terms to make common factors, make sure there is a + sign between the pairs.

$9 {x}^{3} - 36 {x}^{2} - 25 x + 100 \text{ = } \left(9 {x}^{3} - 36 {x}^{2}\right) + \left(- 25 x + 100\right)$

=$9 {x}^{2} \left(x - 4\right) \textcolor{m a \ge n t a}{+} 25 \left(\textcolor{b l u e}{- x + 4}\right)$

=$9 {x}^{2} \left(x - 4\right) \textcolor{m a \ge n t a}{-} 25 \left(\textcolor{b l u e}{x - 4}\right) \leftarrow \text{ }$ note sign change.

=$\left(x - 4\right) \left(9 {x}^{2} - 25\right)$

=$\left(x - 4\right) \left(3 x + 5\right) \left(3 x - 5\right)$