Mysterious polynomial

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.

×