Let $f$ be a cubic polynomial such that $f(0) = 0$, $f(1) = 0$, $f(2) = 0$, and $f(3)=0$. What is the sum of the coefficients of $f$?

 Feb 27, 2024

A cubic polynomial, by the fundamental theorem of algebra, will have EXACTLY three roots (which generalizes to an nth degree polynomial to have n complex roots). Clearly, in this problme, there are four roots, so a cubic polynomial f does not exist, and all coefficients would be 0. Thus, the sum of the coefficients is 0.

 Feb 27, 2024

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