# Reduce me non-constantly

**Number Theory**Level 4

What are the last three digits of the product of absolute values of all integers \(n,\) such that the polynomial \[f_n(x)=x^5+nx^3-3x^2-9\] can be expressed as a product of two non-constant polynomials with integer coefficients?

**Details and assumptions**

The last three digits of the number 1023 are 023. You can type in your answer as 023 or 23.

If you think that the integers \( 2, -2, -3, -4 \) satisfy the conditions, then the product of absolute values of all these integers is \( 2 \times 2 \times 3 \times 4 \).

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