Question 1094265
Try to factor and see if that helps  (in case numerator is factorable).
<pre>
            3x^3    -24x^2   221x   -1768
       _____________________________________________
x+8    |    3x^4     0x^3    29x^2    0x    36
       |    3x^4    24x^3
       |___________________________________________
            0      -24x^3   29x^2
                   -24x^3  -192x^2
                  ---------------
                    0     221x^2     0x
                          221x^2  1768x 
                         --------------
                           0    -1768x     36
                                -1768x   -14144 
                                ----------------
                                 0      14180, the remainder
</pre>
{{{3x^4-24x^3+221x-1768-14180/(x+8)}}}