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Galois Theory, 4th Edition
book

Galois Theory, 4th Edition

by Ian Nicholas Stewart
March 2015
Intermediate to advanced content levelIntermediate to advanced
344 pages
10h 18m
English
Chapman and Hall/CRC
Content preview from Galois Theory, 4th Edition
52 Factorisation of Polynomials
(3) However, t
2
2 is reducible over the larger subfield R, for now
t
2
2 = (t
2)(t +
2)
This shows that an irreducible polynomial may become reducible over a larger sub-
field of C.
(4) The polynomial 6t + 3 is irreducible in Z[t]. Although it has factors
6t + 3 = 3(2t + 1)
the degree of 2t + 1 is the same as that of 6t + 6. So this factorisation does not count.
(5) The constant polynomial 6 is irreducible in Z[t]. Again, 6 = 2 ·3 does not count.
Any reducible polynomial can be written as the product of two polynomials of
smaller degree. If either of these is reducible it too can be split up into factors of
smaller degree ...
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Publisher Resources

ISBN: 9781482245837