Question 172698: could you please explain this problem step by step.
Determine whether x-1 or x+1 is a factor of
x^100 - 4x^99 + 3
I would really appreciate your help!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! could you please explain this problem step by step.
Determine whether x-1 or x+1 is a factor of
x^100 - 4x^99 + 3
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Set x^100 - 4x^99 + 3 = 0
If x+1 is a factor, then subbing -1 for x will make it zero.
If x-1 is a factor, then subbing +1 for x will make it zero.
In either case, x^100 is +1.
For (x+1):
1 - 4*(-1)^99 + 3 =? 0
1 + 4 + 3 = 8, so that's no good.
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For (x-1):
1 - 4*1 + 3 =? 0
0 = 0, so it is (x-1) that's a factor.
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