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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? Please explain.

 Jul 19, 2018

Best Answer 

 #1
avatar+27653 
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With four values given, the polynomial could be a cubic:

 

f(x) = ax3 + bx2 + cx + d

 

Replace x by 1 to get: 

f(1) = a + b + c + d. ie the sum of the coefficients.

 

But we are told that f(1) is 32, Hence this is the sum of the coefficients.

 

This reasoning holds even if the polynomial is not a cubic, as replacing x by 1 simply results in f(1) being the sum of the coefficients!

 Jul 20, 2018
 #1
avatar+27653 
+2
Best Answer

With four values given, the polynomial could be a cubic:

 

f(x) = ax3 + bx2 + cx + d

 

Replace x by 1 to get: 

f(1) = a + b + c + d. ie the sum of the coefficients.

 

But we are told that f(1) is 32, Hence this is the sum of the coefficients.

 

This reasoning holds even if the polynomial is not a cubic, as replacing x by 1 simply results in f(1) being the sum of the coefficients!

Alan Jul 20, 2018

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