+19 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 \(f \)?
+118667 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
\(f(x)=ax^n+bx^{n-1}+cx^{n-2}+\dots+47\\ f(1)=a+b+c+\dots +47=32\\ so\\ a+b+c+\dots +47=32\\ a+b+c+\dots +(\text{coefficient of x)}=32-47\\\)
