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 KŒxŁ , and the addition and multiplication operations on KŒxŁ 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 KŒxŁ . 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 veriﬁed by straightforward computations, using the deﬁnitions of the operations and the corresponding properties of the operations in K ....
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 Fall '08
 EVERAGE
 Algebra, Polynomials, Addition, Natural number, bj /x

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