Question 1047962
This works about the same way as regular base-ten long division.  I will only do question "b".

<pre>
                 4x            -1
         _____________________________________________
         |
         |       4x^3         -x^2       +16x      +0
x^2+4    |
         |      4x^3           0x^2      16x
          -------------------------------------
                 0            -x^2       0x         0
                              -x^2      0x         -4
                            --------------------------
                                0        0         4
</pre>

Main quotient is 4x-1 and remainder is 4; and since the denominator is same as the divisor,  full quotient result is  {{{4x-1+4/(x^2+4)}}}.