How do you factor completely #18x^4+9x^3-20x^2#?
Let's start with the original:
We can first factor out
From here, we need to find factors for the terms within the brackets in the form of
and there's some trial and error to this.
Let's play with
We have a different story with
So let's see if we can find a combo that works:
For a=6, b=-4, c=3, d=5; ac = 18, bd = -20, ad+bc = 30-12=18
For a=6, b=-5, c=3, d=4; ac = 18, bd=-20, ad+bc = 24-15=9
Ok - found a combo that works. Let's factor: