Stuck on Polynomial Division Problem Trying to find the quotient and remainder of the problem below..but keep getting to wrong. Could someone demonstrate how to solve this correctly?
 A: It seems that you would have saved yourself a little confusion if you had simply set up the polynomial long division as follows:
$$x - 2\; \overline{|\;\;x^5 - x^4 - 4x^3 + \color{maroon}{0x^2} + 2x + 3\;}$$
and proceeded from there. (I.e., by writing in and accounting for the "implicit term" $\color{maroon}{0\cdot x^2}$, you would have kept the division properly aligned, and saved yourself a bit of a headache.)
A: Let's see.  In this division, i have used base $x$ and long division.  Unlike ordinary long division, i have taken the negative of the subtractions, and added them.  This is quicker when there are mixed signs involved.
The answer is read off as $x^4+x^3-2z^2-4x-6$ remainder $-9$
           (5)   (4)  (3)(2)  (1) (0)

                  1   1  -2   -4  -6    rem 9
          --------------------------       
    1, -2 )  1   -1  -4   0   2    3       
            -1    2
                  1  -4                        
                 -1   2
                 ======                    
                     -2    0
                      2   -4
                          -4    2
                           4   -8
                               -6  3
                                6 -12
                                   -9

      1    1  -2   -4   -6 
          -2  -2    4    8   12
                             -9   remainder
       1   1  -4    0    2    3

