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?
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.
+8 
