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)

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Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva