Rewrite x^3+5x^2+3x-10/x+4 in the form q(x)+r(x)/b(x)

One way to do it: Find coefficients such that





So, we have





This can also be done with long or synthetic division. Just to verify the result above, synthetic division yields

-4  |  1   5   3   -10
.    |      -4  -4      4
- - - - - - - - - - - - - -
.    |  1   1  -1     -6

which translates to



as required.

Here, , , and .