How do you factor 252v + 48v ^2 -12v ^3?

Apr 10, 2015

Let's modify the expression to get it in Standard Form first.

$252 v + 48 {v}^{2} - 12 {v}^{3}$

$= - 12 {v}^{3} + 48 {v}^{2} + 252 v$

12v is a common factor to all the terms in the above expression. So we can write it as:

$= 12 v \left(- {v}^{2} + 4 v + 21\right)$

 =-12vcolor(red)((v ^2 - 4v - 21)  -------(1)

color(red)(v ^2 - 4v - 21
$= {v}^{2} - 7 v + 3 v - 21$
$= v \left(v - 7\right) + 3 \left(v - 7\right)$
$= \left(v - 7\right) \left(v + 3\right)$ -------(color(red)(2))

Substituting $\left(\textcolor{red}{2}\right)$ in (1), we get

color(green)( -12v*(v - 7)* (v+3)

The above is the factorised form of $252 v + 48 {v}^{2} - 12 {v}^{3}$