I have a polynomial $P(x)$ with positive integer coefficients. You can give me a dollar and an integer x, and I will tell you $P(x)$. What’s the minimum amount of money you need to determine my polynomial?

Extra Credit

What if $x$ doesn’t have to be an integer?

What if my polynomial $P(x)$ doesn’t have integer coefficients?

What if my polynomial $P(x)$ doesn’t have have positive coefficients?