\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A = X^3 - 1\), \(B = X^2 + X + 1\), \(C = X - 1\) in \(\mathbb{R}[X]\).
  1. Verify that \(B \mid A\) and \(C \mid A\).
  2. Using the linear-combination property, deduce that \(B\) divides \(A - X B\) and that \(C\) divides \(A + B C\).

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