It's x3−3x2+9x−298, with remainder 87.
First way to do it is a standard long division algorithm, I guess you know that. In short, you divide x4 with 8x (getting x38), then multiply that with 8x+24 (getting x4+3x3), and subtract that from x4−2x (getting −3x3−2x). Then you do the same thing with that result instead of starting numerator, until you get a single number that cannot be divided by 8x - and that number is 87.
Second way is more interesting, and uses Horner's algorithm. It's easier to apply, but harder to see why it works. It works only when denominator is x−α for some α, so we'll divide by x+3 (α being −3), and then divide by 8 separately.
You make a table with 1,0,0,−2,0 (coefficients of numerator) in the first row, and in the second row, drop 1, multiply by α(=−3) and add 0 (getting −3, then multiply that by α and add next 0 (getting 9), multiply that by α and add −2 (getting −29), and multiply that by α and add the last 0 (getting 87). Entries except the last in the second row are the coefficients of quotient (remember that they still have to be divided by 8), and the last entry is the remainder.
The whole process is explained at http://en.wikipedia.org/wiki/Synthetic_division.
