SOLUTION: Use long division to find the quotient and remainder when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1

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Question 169236: Use long division to find the quotient and remainder when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Use long division to find the quotient and remainder when 
2x%5E5%2B4x%5E4-x%5E3-x%5E2%2B7 is divided by 2x%5E2-1

We must fill in gaps in powers with terms with 0
coefficients. I also will put in 1-coefficients:

Write:
2x%5E5%2B4x%5E4-x%5E3-x%5E2%2B7 as 2x%5E5%2B4x%5E4-1x%5E3-1x%5E2%2B0x%2B7

and

2x%5E2-1 as 2x%5E2%2B0x-1


                         1x3 + 2x2 +  0x +  .5 
            ---------------------------------- 
2x2 + 0x - 1)2x5 + 4x4 - 1x3 - 1x2 +  0x +   7
             2x5 + 0x4 - 1x3
             ---------------
                   4x4 + 0x3 - 1x2
                   4x4 + 0x3 - 2x2
                   ---------------
                         0x3 + 1x2 +  0x
                         0x3 + 0x2 +  0x
                         ---------------
                               1x2 +  0x +   7
                               1x2 +  0x -  .5
                               ---------------
                                           7.5


                            7.5
Answer:  x3 + 2x2 + .5 + ----------
                          2x² - 1
 
Edwin