### Solving 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