Number of positive integers `x` for which `f(x)=x^3-8x^2+20 x-13` is a prime number is______.

Explanation

To solve the problem of finding the number of positive integers \( x \) for which \( f(x) = x^3 - 8x^2 + 20x - 13 \) is a prime number, we will follow these steps:

### Step 1: Factor the polynomial
We start by checking if \( x = 1 \) is a root of the polynomial \( f(x) \).

\[ f(1) = 1^3 - 8(1^2) + 20(1) - 13 = 1 - 8 + 20 - 13 = 0 \]
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