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?.
"Lemma A" = the theorem offered in the Hint
If a polynomial of degree 2 or 3 is reducible at least one of its factors must ...
Irreducible Polynomials are investigated.