How do you factor completely 12z^2+7z-12?

May 19, 2018

See below

Explanation:

Two alternatives: use quadratic formula or complete square (a little bit complicate in this case). The use of Riffini's method is also available but in this case is not quite evident

$12 {z}^{2} + 7 z - 12 = 0$

$z = \frac{- 7 \pm \sqrt{49 + 576}}{24} = \frac{- 7 \pm 25}{24}$ from here two solutions

$z = \frac{3}{4}$ and $z = - \frac{4}{3}$

Then factoring is $\left(z - \frac{3}{4}\right) \left(z + \frac{4}{3}\right) = 12 {z}^{2} + 7 z - 12$

May 19, 2018

$\left(3 z + 4\right) \cdot \left(4 z - 3\right)$

Explanation:

$12 {z}^{2} + 7 z - 12$

=$12 {z}^{2} + 16 z - 9 z - 12$

=$4 z \cdot \left(3 z + 4\right) - 3 \cdot \left(3 z + 4\right)$

=$\left(3 z + 4\right) \cdot \left(4 z - 3\right)$