Let \(n\) be a positive integer. Then \(x^2 +1\) is a factor of



  1. all \(n\);

  2. even \(n\);

  3. odd \(n\);

  4. \(n \geq 3\);

  5. no values of \(n\).

What ideas can we use if we know \(x^2+1\) is a factor?

What is the same and what is different about this question compared to other polynomial factorisation questions?