\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}_3[X]\), complete the free family \(\bigl(1 + X, X^2\bigr)\) into a basis of \(\mathbb{R}_3[X]\) using the canonical basis \((1, X, X^2, X^3)\).
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