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 207959: How can I do the factoring of the following: N to the forth power minus 4N to the 3rd power plus n minus 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
n%5E4-4n%5E3%2Bn-4 Start with the given expression


%28n%5E4-4n%5E3%29%2B%28n-4%29 Group like terms


n%5E3%28n-4%29%2B1%28n-4%29 Factor out the GCF n%5E3 out of the first group. Factor out the GCF 1 out of the second group


%28n%5E3%2B1%29%28n-4%29 Since we have the common term n-4, we can combine like terms


%28n%2B1%29%28n%5E2-n%2B1%29%28n-4%29 Now factor n%5E3%2B1 to get %28n%2B1%29%28n%5E2-n%2B1%29 (hint: use the sum of cubes formula)


%28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29 Rearrange the terms.


So n%5E4-4n%5E3%2Bn-4 completely factors to %28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29


In other words, n%5E4-4n%5E3%2Bn-4=%28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29