Question 111643
<pre><font size = 6 color = "darkblue"><b>
{{{(2x^5+3x^4+8x^3+26x^2+21x)/(2x^2+3x)}}}

Factor x out of the top and 
factor x out of the bottom:

{{{(x(2x^4+3x^3+8x^2+26x+21))/(x(2x+3))}}} 

Cancel the x's

{{{(2x^4+3x^3+8x^2+26x+21)/(2x+3)}}}

Now use long division:

               x³ + 0x² +  4x +  7 
       ———————————————————————————
2x + 3 )2x<font size = 3><sup>4</sup></font> + 3x³ + 8x² + 26x + 21
        2x<font size = 3><sup>4</sup></font> + 3x³ 
        —————————  
              0x³ + 8x²
              0x³ + 0x²
              ————————— 
                    8x² + 26x
                    8x² + 12x
                    —————————
                          14x + 21
                          14x + 21
                          ———————— 
                                 0

So the answer is x³ + 0x² + 4x + 7, or 
omitting the zero term:

                 x³ + 4x + 7

Edwin</pre>