Question 1044920
Polynomial division works the same way as regular base-ten division but often is easier.

<pre>
             x^2    -x     1
        _______________________________________________
x^3+1   |    x^5   -x^4   x^3    2x^2    -x    4
        |
        |    x^5    0x^4  0x^3   x^2
        -----------------------------
              0    -x^4  x^3    x^2     -x
                   -x^4  0x^3  0x^2    -x
                  ------------------------
                   0     x^3   x^2     0      4
                         x^3   0x^2    0x     1
                        ------------------------
                          0   x^2      0     3


NOTE that the bottom row here shows degree 2, which is less than the degree 3 of the divisor!  Bottom row here represents the REMAINDER.
</pre>
Remainder is {{{x^2+3}}}, which represents  {{{(x^2+3)/(x^3+1)}}}, just the way you would do if you were dividing plain base-ten numbers.