SOLUTION: How can I do the factoring of the following: N to the forth power minus 4N to the 3rd power plus n minus 4

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Question 207960: How can I do the factoring of the following: N to the forth power minus 4N to the 3rd power plus n minus 4
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How can I do the factoring of the following: N to the forth power minus 4N to the 3rd power plus n minus 4
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n%5E4+-+4n%5E3+%2B+n+-+4
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Inspection is a start. Since the coefficients are 1,-4,1,-4, try 1 and -1, and 4 and -4.
If n=-1, that's an obvious zero, since it's 1+4-1-4.
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Divide by (n+1)
= %28n%2B1%29%2A%28n%5E3+-5n%5E2+%2B+5n+-+4%29
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Try n = 4: 64 - 80 + 20 - 4 = 0 so (n-4) is a factor.
=%28n%2B1%29%2A%28n-4%29%2A%28n%5E2+%2B+n+%2B+1%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How can I do the factoring of the following:
N to the forth power minus 4N to the 3rd power plus n minus 4
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N^4 - 4N^3 + N - 4
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Factor the 1st two terms and the last two terms separately:
N^3(N-4) + (N-4)
Factor again to get the final answer:
(N-4)(N^3+1)
Factor again:
(N-4)(N+1)(N^2-N+1)
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Cheers,
Stan H.