Hey,
Please can someone help explain the following to me.
Given the field:
It has the following elements in it: 0, 1, 2, x, 2x, x + 1, x + 2, 2x +1 and 2x + 2.
It's also a finite field, because x^2 + 1 is irreducible mod 3.
What I need to understand is how to show that a given polynomial is irreducible in a given field, I don't know how to prove in this case that x^2 + 1 is irreducible.
Also if I was just given a field, how would I find all irreducible polynomials within it?
I'm a tad confused
with my current knowledge I just about know how to work out if something is a field or not, however my polynomial knowledge is pretty limited and I don't really know which techniques i need to be using here.
Thanks for any help.
Please can someone help explain the following to me.
Given the field:
It has the following elements in it: 0, 1, 2, x, 2x, x + 1, x + 2, 2x +1 and 2x + 2.
It's also a finite field, because x^2 + 1 is irreducible mod 3.
What I need to understand is how to show that a given polynomial is irreducible in a given field, I don't know how to prove in this case that x^2 + 1 is irreducible.
Also if I was just given a field, how would I find all irreducible polynomials within it?
I'm a tad confused
with my current knowledge I just about know how to work out if something is a field or not, however my polynomial knowledge is pretty limited and I don't really know which techniques i need to be using here.Thanks for any help.
