and write it like this, as linear factors multiplied and summed:
And the coefficients are:
I found it interesting that all of these coefficients are real numbers, I'm not sure if it's ever necessary to use imaginary numbers or not. I called it extruding the polynomial because it reminds me of the way steel can be shaped by squeezing it through an aperture, in this case a linear factor aperture :).
You might wonder why I didn't try to make z:
Maple wasn't able to solve this one even with so many less variables...