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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 \(f \)?

 Aug 30, 2021
 #1
avatar+114536 
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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

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

 Sep 6, 2021

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