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 $f$?

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1 Answer

Let f(x)=a0+a1x+a2x^2+a3x^3+...

f(0)=a0=47; f(1)=47+a1+a2+...=32, so a1+a2+...=32-47=-15.

The sum of the coefficients of the x terms is -15.
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