\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A = X - 1\) and \(B = X + 1\) in \(\mathbb{R}[X]\). Exhibit three explicit common multiples of \(A\) and \(B\) of degrees \(2\), \(3\), and \(4\) respectively, and verify in each case that the multiple is divisible by \(A \vee B = (X - 1)(X + 1)\).
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