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Irreducible Polynomials

Prove that a polynomial f(x) of degree 2 or 3 over a field F is irreducible if and only if f(a) different of 0 for all a belongs F.
Hint: Use the following theorem that a polynomial f(x) has x-a as a factor if and only if f(a)=0.

Please can you explain this step by step. and Can you give me examples.

Can you explain why this does not happened with polynomial of degree 4?.

Solution Preview

"Lemma A" = the theorem offered in the Hint

Lemma B:
If a polynomial of degree 2 or 3 is reducible at least one of its factors must ...

Solution Summary

Irreducible Polynomials are investigated.