\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}_3[X]\), complete the basis \((X, X^2 - 1)\) of \(F = \mathrm{Vect}(X, X^2 - 1)\) into a basis of \(\mathbb{R}_3[X]\) adapted to \(F\).
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