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.

hellospeedmind Jul 19, 2018

#1**+2 **

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

f(x) = ax^{3} + bx^{2} + 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

#1**+2 **

Best Answer

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

f(x) = ax^{3} + bx^{2} + 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