1. ## Irreducible polynomial

Write down an irreducible polynomial of degree 3 over the field F3 of 3 elements.

I have a very vague idea about irreducible polynmials. I think it is one which cannot be factorized completely.

So if i give an answer to this as x^3 +1, would I be right. or say, 2x^3 +1.

2. Originally Posted by poorna
Write down an irreducible polynomial of degree 3 over the field F3 of 3 elements.

I have a very vague idea about irreducible polynmials. I think it is one which cannot be factorized completely.

So if i give an answer to this as x^3 +1, would I be right. or say, 2x^3 +1.
no, both polynomials that you gave have a root in your field. one example is $x^3+x^2+2.$ note that a polynomial of degree 3 over a field is irreducible if and only if it has no root in that field.