\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}_3[X]\), set \(F = \{P \in \mathbb{R}_3[X] : P(0) = 0\}\) and \(G = \mathbb{R}_0[X]\) (constants). Show that \(F \oplus G = \mathbb{R}_3[X]\).
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