SOLUTION: How many positive integers n are such that the value of the expression n^3 -14n^2 + 64n

SOLUTION: How many positive integers n are such that the value of the expression n^3 -14n^2 + 64n - 93 is a prime number?

Question 550132: How many positive integers n are such that the value of
the expression n^3 -14n^2 + 64n - 93 is a prime number?
Answer by richard1234(7193) (Show Source): 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:

n = 2 --> -13
n = 4 --> 3
n = 5 --> 2
n = 6 --> 3

The values n = 4, 5, 6 produce prime numbers, so the answer is 3.

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