I don't think this simplifies... am I wrong?

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

Re: I don't think this simplifies... am I wrong?

a) it's a typo

b) the "simplification" being called for is of the form: quotient + remainder/(x - 2).

Re: I don't think this simplifies... am I wrong?

The only purpose to trying to factor the numerator would be to try to cancel the term in the denominator. And you know that the denominator is x- 2 so the only factor of interest is x- 2. Further, x- 2 will be a factor of the numerator only if setting x= 2 in the numerator makes it equal. So all you really needed to do was calculate 4(16)+ 3(8)- 2(4)+ 1= 32+ 24- 8+ 1= 49, not 0.

Re: I don't think this simplifies... am I wrong?

Excellent points HallsofIvy and Deveno, and thanks so much for such a quick reply :)