\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A, B \in \mathbb{K}[X]\) with \(B \ne 0\), and \(R \in \mathbb{K}[X]\) with \(\deg R < \deg B\). Show that the Euclidean division of \(A B + R\) by \(B\) gives quotient \(A\) and remainder \(R\).
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