I would like to prove that x² + 2x - 1 is irreducible over ℤ/5ℤ.
Not really sure how to go with that, it's probably related to finding roots in the field since it's already monic, right ?
Thank you.
2026-04-09 10:54:53.1775732093
Proving a polynomial is irreducible over a field.
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Yes, if a quadratic is reducible, then it factors into two linear factors, so it has at least one root (possibly repeated).
So you can just plug in every number to see if it has a root.