# How do you factor 12x^2+13x-14?

May 20, 2015

You can find its roots and then turn them into factors.

Let's use Bhaskara to find the roots:

$\frac{- 13 \pm \left(169 - 4 \left(12\right) \left(- 14\right)\right)}{24}$
$\frac{- 13 \pm 29}{24}$
${x}_{1} = - \frac{7}{4}$, which is the same as the factor $\left(4 x + 7\right) = 0$
${x}_{2} = \frac{2}{3}$, which is the same as the factor $\left(3 x - 2\right) = 0$

$\left(4 x + 7\right) \left(3 x - 2\right)$