I've been trying to get my head around the method that my lecturer uses, it's not the regular one we used in secondary school, and it's not synthetic division. You put the larger of the two on the left and the smaller on the right, and then figure out what the smaller is multiplied by to get the larger + remainder.
So for example to divide x^4-x^3+x-1 by x^4-x^3+x-1 you would do:
Then take x^3-x^2+x-1 to the next line and divide by the remainder (-x^2+2x-1)
I understand it for small ones like that, but when it's larger ones like x^10 or where the coefficient of x isn't 1 I can't do them...