SOLUTION: Use synthetic division to perform the division. {{{(x^5-1)/(x-1)}}}

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Question 895162: Use synthetic division to perform the division.
%28x%5E5-1%29%2F%28x-1%29
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E5-1%29%2F%28x-1%29

Write x%5E5-1 as x%5E5%2B0x%5E4%2B0x%5E3%2B0x%5E2%2B0x%5E1-1

We change the sign of -1 to +1

1 | 1  0  0  0  0 -1
  |    1  1  1  1  1
    1  1  1  1  1  0

Answer:  Start with x to 1 less power than the x%5E5 in the denominator:

1x%5E4%2B1x%5E3%2B1x%5E2%2B1x%5E1%2B1

Eliminating the understood 1's

x%5E4%2Bx%5E3%2Bx%5E2%2Bx%2B1

Edwin