SOLUTION: Which of the following expressions must be positive for all values of n? n^2 + n n^3 n^3 + n n^3 + n^2 n^4 + n^2 + 1

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Question 955615: Which of the following expressions must be positive for all values of n?
n^2 + n
n^3
n^3 + n
n^3 + n^2
n^4 + n^2 + 1
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Interesting, no minuses and no negations.

Try assuming n=-k, and that k is a positive number. What happens when n=-k in each of those listed expressions?

Here is the first one:
%28-k%29%5E2%2B%28-k%29
k%5E2-k
Maybe a factorization,
k%28k-1%29
This can be negative for any k%3C1, so this n%5E2%2Bn does not fit the needed description.