document.write( "Question 955615: Which of the following expressions must be positive for all values of n?\r
\n" ); document.write( "\n" ); document.write( " n^2 + n
\n" ); document.write( " n^3
\n" ); document.write( " n^3 + n
\n" ); document.write( " n^3 + n^2
\n" ); document.write( " n^4 + n^2 + 1
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #583849 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
Interesting, no minuses and no negations.\r
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\n" ); document.write( "\n" ); document.write( "Try assuming n=-k, and that k is a positive number. What happens when n=-k in each of those listed expressions?\r
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\n" ); document.write( "\n" ); document.write( "Here is the first one:
\n" ); document.write( " $\"%28-k%29%5E2%2B%28-k%29\"$
\n" ); document.write( " $\"k%5E2-k\"$
\n" ); document.write( "Maybe a factorization,
\n" ); document.write( " $\"k%28k-1%29\"$
\n" ); document.write( "This can be negative for any $\"k%3C1\"$ , so this $\"n%5E2%2Bn\"$ does not fit the needed description. \n" ); document.write( "

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