Let $f : \mathbb{C} \to \mathbb{C}$ be a D4312: Complex polynomial function such that

(i)	$N \in \{ 1, 2, 3, \ldots \}$ is a D5094: Positive integer
(ii)	$r_0, r_1, \ldots, r_N \in \mathbb{C}$ are each a D1207: Complex number
(iii)	\begin{equation} r_N \neq 0 \end{equation}
(iv)	\begin{equation} f(z) = \sum_{n = 0}^N r_n z^n \end{equation}

Then \begin{equation} \exists \, \lambda_0, \lambda_1, \, \ldots, \, \lambda_N \in \mathbb{C} : \forall \, z \in \mathbb{C} : f(z) = \lambda_0 \prod^N_{n = 1} (z - \lambda_n) \end{equation}