How do you factor # 6uv - 3v^3 + 4u - 2v^2#?
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:
Examine each for possible extraction of common factors
The first possibilities doesn't have any useful factors (other than 2) in the terms
So let's try the other pairing