- Find all monic irreducible polynomials of degree 2 over Z3.
x^2 + 1, x^2 + x + 2,x^2 + 2x + 2, this is the answer from the book. But I have no idea what it actually means. Can someone explain?
-Wooi-Chen Ng
Monic means the leading coefficient is 1. Degree two means the highest power is 2. And irreducible means it doesn't factor interestingly. So each polynomial has x^2 as the leading term. Then we just add all the possible combinations of linear polynomials in Z3 and see which do not factor.
-Allen
Since the Reducibility Test for Degrees 2 and 3 (Theorem 17.1) is an if-and-only-if statement, it can also be used instead of trying to factor to determine which ones are the irreducible ones.
-Josh
