Question

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

Answer 1

`-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.