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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 1, 2020
edited by Guest  Jul 1, 2020
edited by Guest  Jul 1, 2020
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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 1, 2020

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