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Unformatted text preview: this out. Example 1.8.1. .2x 3 C 4x C 5/ C .5x 7 C 9x 3 C x 2 C 2x C 8/ D 5x 7 C 11x 3 C x 2 C 6x C 13; and .2x 3 C 4x C 5/.5x 7 C 9x 3 C x 2 C 2x C 8/ D 10x 10 C 20x 8 C 25x 7 C 18x 6 C 2x 5 C 40x 4 C 65x 3 C 13x 2 C 42x C 40: K can be regarded as subset of Kx , and the addition and multiplication operations on Kx extend those on K ; that is, for any two elements in K , their sum and product as elements of K agree with their sum and product as elements of Kx . The operations of addition and multiplication of polynomials satisfy properties exactly analogous to those listed for the integers in Proposition 1.6.1 ; see Proposition 1.8.2 on the next page. All of these properties can be veried by straightforward computations, using the denitions of the operations and the corresponding properties of the operations in K ....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Polynomials

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