Question 983557
Multiply the dividend and the divisor by 27, simplify, and then use polynomial division.


{{{81x^4+54x^3-9x^2-3x+2}}}  divided by  {{{27x+18}}};
All whole number coefficients, much easier to handle this way.


---


<pre>
                  3x^3       0     -(1/3)x
             |_______________________________________
             |
27x-18    |    81x^4     54x^3    -9x^2     2
               81x^4     54x^3
                _______________
               0          0        -9x^2
                          0          0
                          _____________
                                    -9x^2     2
                                    -9x^2     6
                                    __________
                                      0      -4
</pre>


Quotient is  {{{highlight(3x^3-(1/3)x-4/(27x-18))}}}.