How do you factor #-6cf + 8c^2d - 9df + 12cd^2#?

1 Answer
George C.
Jan 1, 2017

#-6cf+8c^2d-9df+12cd^2 = (2c+3d)(4cd-3f)#

Explanation:

Given:

#-6cf+8c^2d-9df+12cd^2#

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping:

#-6cf+8c^2d-9df+12cd^2 = (-6cf+8c^2d)+(-9df+12cd^2)#

#color(white)(-6cf+8c^2d-9df+12cd^2) = 2c(-3f+4cd)+3d(-3f+4cd)#

#color(white)(-6cf+8c^2d-9df+12cd^2) = (2c+3d)(4cd-3f)#

The remaining quadratic term is irreducible.

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