Let P(x) be a polynomial with non-negative integer coefficients such that P(0)=33, P(1)=40, and P(9)=60000. Find P(2).

The last coefficient is 33

60000 - 33 = 59967

59967 = 101230 (Base 9)

So, P(x) can be x^5 + x^3 + 2x^2 + 3x + 33

And because we know that all the coefficients except the last are non-negative integers less than 9 (in fact, less than or equal to 7), this is the only possible P(x).

*Edited on ***August 16, 2024, 2:39 pm**