# How do you factor 8x^2 +2x - 15?

Mar 24, 2016

$\left(4 x - 5\right) \left(2 x + 3\right)$

#### Explanation:

You could always try using the quadratic formula, but in this case it may be easier to expand the trinomial and factor out common terms.

First multiply the coefficient of the ${x}^{2}$ term, $\left(8\right)$ with the constant, $\left(- 15\right)$

$\left(8\right) \left(- 15\right) = - 120$ Now look for two numbers which multiply together to get $- 120$ and at the same time have a sum of $+ 2$.

In this case, $\left(- 10\right) \left(12\right) = - 120$ and $- 10 + 12 = 2$

Using these two numbers I can expand the original expression:

$8 {x}^{2} + 2 x - 15 = 8 {x}^{2} - 10 x + 12 x - 15$. Now, in this expanded expression, group the first two terms and the last two terms together

$\left(8 {x}^{2} - 10 x\right) + \left(12 x - 15\right)$. Now factor out common terms:

$2 x \left(4 x - 5\right) + 3 \left(4 x - 5\right)$. Notice the common factor is $\left(4 x - 5\right)$. So

$\left(4 x - 5\right) \left(2 x + 3\right)$ is the factored form of the trinomial.