a) it's a typo
b) the "simplification" being called for is of the form: quotient + remainder/(x - 2).
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?
(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?
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.