How would you write 1 - x^4 before you divide it by x - 1?

Order your terms by the powers of exponents in decreasing order (as is the case with pure number division hundreds, tens, ones, tenths, etc, etc) as x^n, x^n-1 etc ...

(-x^4+1) / (x-1)

-x^3 rem - x^3-1

-x^2 rem - x^2-1

-x rem - x-1

-1 rem 0

(x-1) (-x^3-x^2-x-1)

(x-1) (-x^3-x-x^2-1)

(x-1) (-x (x^2+1) - 1 (x^2+1))

(x-1) (-x-1) (x^2+1)