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

Jan 19, 2016

$\left(5 x - 4\right) \left(3 x + 2\right)$
$15 {x}^{2} - 12 x + 10 x - 8$

#### Explanation:

Check for a product what product:
$\left(- 2 - 3 x\right) \left(4 - 5 x\right)$
Multiply and test:
$- 8 - 12 x + 10 x + 15 {x}^{2}$
Multiply by negative one if you like and have the factors in the answer form
Wich recovers the original quadratic equation

Jan 19, 2016

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

#### Explanation:

First, you have to find the zeros of the expression, with the general expression

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x = \frac{2 \pm \sqrt{{2}^{2} - 4 \cdot 15 \cdot 8}}{2 \cdot 15}$

$x = \frac{2 \pm \sqrt{484}}{30}$

$x = \frac{2 \pm 22}{30}$

$x = \frac{24}{30}$ or $x = - \frac{20}{30}$

$x = \frac{4}{5}$ or $x = - \frac{2}{3}$

Finding the zeros we can factorize the expression:

$15 \left(x - \frac{4}{5}\right) \left(x + \frac{2}{3}\right)$

We can continue further to

$5 \left(x - \frac{4}{5}\right) \cdot 3 \left(x + \frac{2}{3}\right)$

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