Been scratching my noggin' over this one foe some time now... this is a problem I am working on in preparation for my state math certification exam for high school math...

My question is, is this a typo perhaps, or is there something I'm missing?

Simplify:

(4x^4 + 3x^3 -2x +1)/(x-2)

I've tried synthetic division with all possible roots (including the missing term), to no avail. Plugging into a TI-89 shows that all 4 roots are complex, which was confirmed by just plugging the coefficients into an online calculator. I know it sounds elementary, but I did look into factoring by grouping, etc. I'm stumped on this one. Is there something I'm missing here?

Thanks