Let f(x) be a polynomial of degree n > 0 in a polynomial ring K[x] overa field K. Prove that any element of the quotient ring K[x]/ (f(x)) is ofthe form g(x) + (f(x)), where g(x) is a polynomial of degree at mostn - 1.

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Answered: Let f(r) be a polynomial of degree n >…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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Let f(r) be a polynomial of degree n > 0 in a polynomial ring K[r] a field K. Prove that any element of the quotient ring K[x]/ (f(x)) the form g(x) + (f(x)), where g(x) is a polynomial of degree at n - 1.