Question 175600
{{{(x^4 - x^3 - 9x^2 +14x - 4) /(x^2 - 3x + 1)}}}
:
your answer of :{{{x^3+2x^2+9x+8}}} is quite wrong the answer cannot have a term with a 3rd degree in it or we would have an {{{x^5}}}term. So the book either has it wrong or you looked at the wrong problem or there is a typo in the problem you gave us.

<pre> 
            x<sup>2</sup>   +2x - 6
            --------------------- 
x<sup>2</sup>-3x+1 )    x<sup>4</sup> - x<sup>3</sup> - 9x<sup>2</sup> -4
          -(x<sup>4</sup> -3x<sup>3</sup>)
          ----------------
                2x<sup>3</sup> - 9x<sup>2</sup>                               
              -(2x<sup>3</sup> - 6x<sup>2</sup>+2x)
                     -------------------          
                     -6x<sup>2</sup>+ 2x -4 
                   -(-6x<sup>2</sup>+ 18x-6)
                    ------------------------
                             -16x+2 remainder                                

Answer: {{{x^2+2x-6+(-16x+2)/(x^2-3x+1))}}}
 </pre>