Word Count : 359

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The given set \( D = \{f(x, y) + g(x, y) i \mid f, g \in \mathbb{Z}[x, y]\} \subseteq \mathbb{C}[x, y] \) represents a subset of polynomials in \( x \) and \( y \) with integer coefficients, where each element of \( D \) is of the form \( f(x, y) + g(x, y) i \), where \( i \) is the imaginary unit. To determine whether \( D \) is a Unique Factorization Domain (UFD), we need to check if every element in \( D \) can ______ __________ ___ ____ ______ _________ ___.
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