# Mysterious polynomial

**Number Theory**Level 4

A polynomial \(f(x)\) with positive integer coefficients satisfies \(f(1)= 12\) and \(f(12)=2080\). Find the last three digits of \(f(10)\).

**Details and assumptions**

We are talking about all the numbers in their decimal representations.

You aren't given any information about the degree of the polynomial, except that it is positive.