\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that in \(\mathbb{R}_3[X]\) (canonical basis \((1, X, X^2, X^3)\) of cardinal \(4\)), the family $$ \bigl(1 + X, X + X^2, X^2 + X^3, 1 + X^3, X - X^2\bigr) $$ is dependent.
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