SOLUTION: (x^5 + y^5) ÷ (x+y)

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Question 983505: (x^5 + y^5) ÷ (x+y)
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Use polynomial division and account for the progression of degrees for x and y. 


The starting arrangement:



      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |



First partial quotient:

      |   x^4
      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |   x^5   x^4*y
       __________________
          0    -x^4*y



      |   x^4    -x^3*y
      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |   x^5   x^4*y
       __________________
          0    -x^4*y     0*x^3*y^2
               -x^4*y     -x^3*y^2
              _______________________
                0         x^3*y^2


      |   x^4    -x^3*y    x^2*y^2
      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |   x^5   x^4*y
       __________________
          0    -x^4*y     0*x^3*y^2
               -x^4*y     -x^3*y^2
              _______________________
                0         x^3*y^2     0*x^2*y^3
                          x^3*y^2     x^2*y^3
                          ______________________
                           0              0



      |   x^4    -x^3*y    x^2*y^2      0           y^4
      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |   x^5   x^4*y
       __________________
          0    -x^4*y     0*x^3*y^2
               -x^4*y     -x^3*y^2
              _______________________
                0         x^3*y^2     0*x^2*y^3
                          x^3*y^2     x^2*y^3
                          ______________________
                           0              0        0*x*y^4
                                          0         0
                                         ___________________
                                                   x*y^4    y^5
                                                    x*y^4     y^5
                                                   ________________
                                                    0        0


      |________________________________________________________________
x+y   |   x^5   0*x^4*y   0*x^3*y^2   0*x^2*y^3    0*x*y^4   y^5
      |


Result of the division is the top line showing the quotient:
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