document.write( "Question 550132: How many positive integers n are such that the value of
\n" ); document.write( "the expression n^3 -14n^2 + 64n - 93 is a prime number? \n" ); document.write( "

Algebra.Com's Answer #358522 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
The expression factors to (n-3)(n^2 - 11n + 31). Since we want a prime number, either n-3 or n^2 - 11n + 31 must be equal to 1 (or -1). Solving for n, we obtain n = 2, 4, 5, or 6. Here are the values we obtain when we replace n into the given expression:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "n = 2 --> -13
\n" ); document.write( "n = 4 --> 3
\n" ); document.write( "n = 5 --> 2
\n" ); document.write( "n = 6 --> 3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The values n = 4, 5, 6 produce prime numbers, so the answer is 3.
\n" ); document.write( " \n" ); document.write( "

\n" );