\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Determine whether the following pairs are coprime in \(\mathbb{R}[X]\). Justify briefly.
  1. \(A = X^3 + 1\), \(B = X^2 + 1\).
  2. \(A = X^3 - 1\), \(B = X^2 + X + 1\).
  3. \(A = X^4 + 1\), \(B = X^2 + 1\).
  4. \(A = X^2 + X + 1\), \(B = X^2 - X + 1\).

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