Since all four terms don't have a common factor we will group them in pairs with common factors.
6uv - 3v^3 + 4u - 2v^2
6uv + 4u - 3v^3 - 2v^2
Take out 2u from the first two terms and -v^2 from the last two terms. The goal is to have a common factor once we take out the GCF's.
2u( 3v + 2) - v^2(3v + 2)
Now we have two terms:
[2u(3v+2)] + [-v^2(3v+2)]
These two terms have a GCF of (3v + 2). Take that out:
(3v + 2)(2u - v^2)
