Examples 6, 7 and 8 are all very helpful
a.) This is irreducible over Q by Eisenstein with p=3. Eisenstein states that if a number divides every co-efficient but the first then it is irreducible. And 3 divides 9, 12, and 6.
c.) This is done the exact same way as a.)
e.) Multiply all co-efficients by 14 and then use Eisenstein with p=3.
-Zach Simpson
Exactly what I did, but I'm not sure what to do with the others except for trial and error computing, which may not be the best method. Does anyone have any hints? -Tim
Would trying to prove b and d to be irreducible with mod 2 work? -Kristie
For b, yes. This is in the chapter somewhere. For d, not sure. -Josh
Could theorem 17.3 be used for d if p=5? - Dan
For part d use the theorem discussed in class. Theorem: Suppose f(x) is contained in Z[x]. If you can find a prime number p such that f(x)modp is irreducible then f itself was irreducible over Q.
--Robertsr 09:59, 13 November 2008 (UTC)
