\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For \(A = (X - 2)^3 (X + 1)^2\) and \(B = (X - 2)(X + 1)^3 (X - 3)\) in \(\mathbb{R}[X]\), compute \(A \wedge B\) and \(A \vee B\) by factorisation, then verify the gcd-lcm relation \((A \wedge B)(A \vee B) = A B\).
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