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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
Chapter 3
Factorisation of Polynomials
Not only is there an algebra of polynomials: there is an arithmetic. That is, there
are notions analogous to the integer-based concepts of divisibility, primes, prime
factorisation, and highest common factors. These notions are essential for any serious
understanding of polynomial equations, and we develop them in this chapter.
Mathematicians noticed early on that if f is a product gh of polynomials of
smaller degree, then the solutions of f (t) = 0 are precisely those of g(t) = 0 together
with those of h(t) = 0. For example, to solve the equation
t
3
6t
2
+ 11t 6 = 0
we can spot the factorisation (t 1)(t 2)(t
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Publisher Resources

ISBN: 9781482245837