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 $f$? This is copied from Alcumus. I just want a hint. Thanks in advance!
Suppose f(x) is a cubic polynomial y = ax^3 + bx^2 + cx + d. Then
d = 47
a + b + c + d = 32
8a + 4b + 2c + d = -13
27a + 9b + 3c + d = 16
==> f(x) = 46/3*x^3 - 57x^2 + 68/3*x + 47.
The sum of the coefficients is 46/3 - 57 + 68/3 = -19.
