# How do you factor by grouping with three terms 252v + 48v ^2 -12v ^3?

Apr 30, 2015

First simplify by extracting the obvious factor of $12 v$
$252 v + 48 {v}^{2} - 12 {v}^{3}$
$= 12 v \left(21 + 4 v - {v}^{2}\right)$
or
$= \left(- 12 v\right) \left({v}^{2} - 4 v - 21\right)$

$21$ can be factored as $3 \times 7$
and the difference between 3 and 7 is 4

so
$= \left(- 12 v\right) \left({v}^{2} + 3 v - 7 v - 21\right)$

$= \left(- 12 v\right) \left(v \left(v + 3\right) - 7 \left(v + 3\right)\right)$

$= \left(- 12 v\right) \left(v - 7\right) \left(v + 3\right)$