How do you factor # 6uv - 3v^3 + 4u - 2v^2#?

1 Answer
Alan P.
May 3, 2015

This method will not work in all cases but it is one way to attempt to find a solution.

Look for two pair of terms with the same ratio between the coefficients of the elements of the pairs.
In this case there are two possibilities:
#6:-3 -= 4:-2#
and
#color(red)(6:4) -= color(blue)(-3:-2)#

Examine each for possible extraction of common factors

The first possibilities doesn't have any useful factors (other than 2) in the terms #4u# and #-2v^2#

So let's try the other pairing
#6uv-3v^3+4u-2v^2#

#=color(red)(6uv+4u) - color(blue)(3v^3+2v^2)#

#= color(red)(2u(3v+2)) - color(blue)(v^2(3v+2))#

#=(2u-v^2)(3v+2)#

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