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

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) (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:

Maybe a factorization,

This can be negative for any , so this does not fit the needed description.
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