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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 $f$?

 Jul 4, 2020
 #1
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Suppose f(x) is a cubic polynomial y = ax^3 + bx^2 + cx + d.  Then

d = 47

a + b + c + d = 32

8a + 4b + 2c + d = -13

27a + 9b + 3c + d = 16

==> f(x) = 46/3*x^3 - 57x^2 + 68/3*x + 47.

 

The sum of the coefficients is 46/3 - 57 + 68/3 = -19.

 Jul 4, 2020
 #2
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I did the same thing but it said -19 was wrong

 Jul 4, 2020

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