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 \(f \)?

uttoki Aug 30, 2021

#1**+1 **

Since f(1)=32

and

f(0)=47

I think that the sum of the coefficients is 32-47 = -15

This is my logic

Since f(0)=47, the constant must be 47 this is not a coefficient

Consider the polynomial to be

\(f(x)=ax^n+bx^{n-1}+cx^{n-2}+\dots+47\\ f(1)=a+b+c+\dots +47=32\\ so\\ a+b+c+\dots +47=32\\ a+b+c+\dots +(\text{coefficient of x)}=32-47\\\)

Melody Sep 6, 2021