B) please it Let K be any field, and let a1,.…,an be pairwise distinct elements of K (that is, a; † ajfor all i+ j). For each i= 1, ...,n, definePi3 (х — а).-(х - а-1) (х— ан1).. (х— аn) € К\x).Note that the (x– a;) factor has been left out of pi, so deg pi = n – 1.(a) Prove that p;(a;)#0 if and only if i= j.(b) Let b1,…..,bk be elements of K (some of them maybe equal). Using part (a),explain how to find a polynomial q E K[x], with deg q

Name: B) please it Let K be any field, and let a1,.…,an be pairwise distinct
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Description: B) please it Let K be any field, and let a1,.…,an be pairwise distinct elements of K (that is, a; † ajfor all i+ j). For each i= 1, ...,n, definePi3 (х — а).-(х - а-1) (х— ан1).. (х— аn) € К\x).Note that the (x– a;) factor has been left out of pi, so

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Answered: (b) Let b1,...,br be elements of K…

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(b) Let b1,...,br be elements of K (some of them maybe equal). Using part (a), explain how to find a polynomial q E K[x], with deg q

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.6: Algebraic Extensions Of A Field

Problem 12E

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