x^{3}+x^{2}+16 is exactly divisible by x, where x is a positive integer. The number of <strong>ALL</strong> such possible values of x is

Explanation

We can rewrite the expression as \frac{x^3+x^2+16}{x} = x^2 + x + \frac{16}{x}. For this to be an integer, 16 must be exactly divisible by x. The positive divisors of 16 are 1, 2, 4, 8, and 16, which gives exactly 5 possible values.

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