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?

Hmm...well......I could be wrong here, but here's what I was thinking:

 

Since  f(0)  =  47 , we know that the constant term is  47 .

 

Since  f(1)  =  32 , we know that  the sum of the coefficients + 47  =  32

 

the sum of the coefficients + 47  =  32   so

the sum of the coefficients  =  -15