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Question 885551: What is f(x) = x^8 - 1 divided by x - 1?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can solve this through synthetic division or by long division.
since the divisor is in the form of (x-a), synthetic division is the way to go.
you need to fill in each missing degree going from degree 8 to degree 1 whether you use synthetic division or not.
your equation of x^8 - 1 becomes:
x^8 + 0x^7 + 0x6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 0x^1 - 1
the result of either synthetic division or long division will get you a result of:
x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1
that's your answer.
you can confirm this solution is correct by multiplying it by (x-1) and you will get x^8 - 1 back again.
the start of your long division would look like this:
x^8 + 0x^7 + 0x6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 0x^1 - 1 divided by (x-1)
the start of your synthetic division would look like this:
1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 - 1 synthetically divided by 1.
if you need a lesson on how to do long division and how to do synthetic division, go to the following links:
long division:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut36_longdiv.htm
synthetic division:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut37_syndiv.htm
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