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#