Question 1043852
You can use either polynomial division or synthetic division.  Synthetic division will be faster.  Here is the work as polynomial division:

<pre>
            3x^3    5x^2     3x     2
      ___________________________________________
x-1   |     3x^4    2x^3    -x^2    -x    -6
      |
      |     3x^4   -3x^3
      |_____________________
             0      5x^3
                    5x^3   -5x^2
                  _______________
                     0     3x^2
                           3x^2   -3x
                          ___________
                           0      2x
                                  2x    -2
                                  _________
                                   0    -4

Notice remainder is {{{-4}}}.

</pre>
Quotient fully is  {{{3x^3+5x^2+3x+2-4/(x-1)}}}.