Suppose $f$ is a polynomial such that $f(0) = 47$, $f(1) = 32$, $f(2) = -13$, and $f(3)=16$. What is the sum of the coefficients of $f$?
The polynomial is f(x) = 16x^3 - 61x^2 + 29x + 46, and the sum of the coefficients is 16 + (-61) + 29 = -16.
