Thanks. Right, there's the Fundamental Theorem of Algebra and also the Quartic Formula (which doesn't particularly interest me because of its cumbersome nature). So my purpose in this exploration isn't necessarily to break new ground; I'm not one to think I can compete with hundreds of years of mathematical research . Rather, I'm more asking a "What if?" just for fun. In the process, I've come across an apparent possibility that I find a bit fascinating. I'm wondering if:

Any 4th degree polynomial of the form:

can be factored into two quadratics of the form:

such that:

, and

I'm not yet sure how useful this approach actually is, but I just plan to keep on working with it until I find out.