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?

2 answers

First, note that the degree of f must be 3. If higher, there are many possible polynomials which will fit the four points.

If f(x) = ax^3+bx^2+cx+d
d = 47
a+b+c+d = 32
8a+4b+2c+d = -13
27a+9b+3c+d = 16

a+b+c+d = 32
all I know is that it's NOT -15... believe me I tried lol