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d) <math>x^5 + 5x^2 + 1</math> | d) <math>x^5 + 5x^2 + 1</math> | ||
e) <math>(5/2)x^5 + (9/2)x^4 + 15x^3 + (3/7)x^2 + 6x + (3/14)</math> | e) <math>(5/2)x^5 + (9/2)x^4 + 15x^3 + (3/7)x^2 + 6x + (3/14)</math> | ||
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Revision as of 17:14, 8 April 2009
Are the following irreducible over Q?
a) $ x^5 + 9x^4 + 12x^2 + 6 $ b) $ x^4 + x + 1 $ c) $ x^4 + 3x^2 + 3 $ d) $ x^5 + 5x^2 + 1 $ e) $ (5/2)x^5 + (9/2)x^4 + 15x^3 + (3/7)x^2 + 6x + (3/14) $
a.) Look at Eisenstein's with p = 3.
b.) A polynomial is irreducible in Q if there's a p such that f(x) mod p is irreducible. Look at p = 2.
c.) See part a.
d.) See part b.
e.) Multiply by 14 then see part a.
--Jniederh 22:12, 8 April 2009 (UTC)
