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Algebra Level 3

\[ \begin{equation} \begin{split} & \dfrac{(x-b)(x-c)(x-d)}{(a-b)(a-c)(a-d)} \\+ & \dfrac{(x-c)(x-d)(x-a)}{(b-c)(b-d)(b-a)} \\ +& \dfrac{(x-d)(x-a)(x-b)}{(c-d)(c-a)(c-b)} \\ +& \dfrac{(x-a)(x-b)(x-c)}{(d-a)(d-b)(d-c)} \end{split} \end{equation} ~=~? \]

Hint: An equation of \(n^ \text{th}\) degree with more than \(n\) roots is an identity. This is studied extensively in the wiki: The method of undetermined coefficients.

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