# How do you factor 3p^2 - 2p - 5?

Jun 20, 2015

$3 {p}^{2} - 2 p - 5 = \left(p + 1\right) \left(3 p - 5\right)$

#### Explanation:

Let $f \left(p\right) = 3 {p}^{2} - 2 p - 5$.

Notice that $f \left(- 1\right) = 3 + 2 - 5 = 0$.

So $\left(p + 1\right)$ is a factor of $f \left(p\right)$

In order to get the $3 {p}^{2}$ and the $- 5$ terms, the other factor must be $\left(3 p - 5\right)$ so

$3 {p}^{2} - 2 p - 5 = \left(p + 1\right) \left(3 p - 5\right)$