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| − | a.) Look at Eisenstein's with p = 3. | + | a.) Look at Eisenstein's with p = 3.<br> |
| − | b.) A polynomial is irreducible in Q if there's a p such that f(x) mod p is irreducible. Look at p = 2. | + | b.) A polynomial is irreducible in Q if there's a p such that f(x) mod p is irreducible. Look at p = 2.<br> |
| − | c.) See part a. | + | c.) See part a.<br> |
| − | d.) See part b. | + | d.) See part b.<br> |
| − | e.) Multiply by 14 then see part a. | + | e.) Multiply by 14 then see part a.<br> |
--[[User:Jniederh|Jniederh]] 22:12, 8 April 2009 (UTC) | --[[User:Jniederh|Jniederh]] 22:12, 8 April 2009 (UTC) | ||
Revision as of 17:12, 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)
