SOLUTION: {{{(2x^5+3x^4+8x^3+26x^2+21x)/(2x^2+3x)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(2x^5+3x^4+8x^3+26x^2+21x)/(2x^2+3x)}}}      Log On


   

Question 111643: %282x%5E5%2B3x%5E4%2B8x%5E3%2B26x%5E2%2B21x%29%2F%282x%5E2%2B3x%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

%282x%5E5%2B3x%5E4%2B8x%5E3%2B26x%5E2%2B21x%29%2F%282x%5E2%2B3x%29

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

%28x%282x%5E4%2B3x%5E3%2B8x%5E2%2B26x%2B21%29%29%2F%28x%282x%2B3%29%29 

Cancel the x's

%282x%5E4%2B3x%5E3%2B8x%5E2%2B26x%2B21%29%2F%282x%2B3%29

Now use long division:

               x³ + 0x² +  4x +  7 
       ———————————————————————————
2x + 3 )2x4 + 3x³ + 8x² + 26x + 21
        2x4 + 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