# Eisenstein Criterion

1. May 3, 2017

### Mr Davis 97

1. The problem statement, all variables and given/known data
Determine the irreducibility $x^2 - 12$

2. Relevant equations

3. The attempt at a solution
By using $p=3$ we see that $x^2 - 12$ is irreducible, because 3 does not divide 1, and 9 does not divide 12. That's easy enough.
But what if I have $x^2 - 16$? Obviously this is factorable, but using p=3, doesn't the Eisenstein criterion tell us that it is irreducible?

2. May 4, 2017

### Staff: Mentor

No, because you cannot apply Eisenstein here: $3 \nmid 16 = a_0$.