Expert: Scott A Wilson - 10/12/2011

Question
4x^5 - 3x^2 + x+1 divided by 2x^3-1

Answer
Notice that the terms are really 4x^5 + 0x^4 + 0x^3 - 3x^2 + x + 1 divided by
2x^3 + 0x^2 + 0x - 1.

Doing synthetic division gives 4 0 0 -3 1 1 divided by 2 0 0 -1.
Since 4/2 is 2, that is the 1st term.
Taking 2(2 0 0 -1) gives 4 0 0 -2.

Subtracting this from 4 0 0 -3 gives 0 0 0 1.
What we have left on top is a remainder, since it is 1 1 1.
That is because there are only 3 terms and we are dividing by 4 terms.

Thus, the answer is 2x^2, remainder x^2+x+1.
Note that we are dividing by something that starts with an x^3,
so it can't be done again.