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

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Answer 1 · 2015-04-10T08:55:17

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

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

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

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

$= 12v(-v ^2 + 4v + 21)$

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

$color(red)(v ^2 - 4v - 21$
$= v^2 - 7v +3v -21$
$= v(v - 7) +3(v -7)$
$= (v - 7) (v+3)$ -------( $color(red)(2))$

Substituting $(color(red)(2))$ in (1), we get

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

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

How do you factor 252v + 48v ^2 -12v ^3252v + 48v ^2 -12v ^3?