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HELP PLS

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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
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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