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Let a E K and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is ƒ(a). (Hint: nome the nefficients of fie write

Let a E K and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is ƒ(a). (Hint: nome the nefficients of fie write

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let a EK and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is f(a). (Hint: name the coefficients of f, i.e. write f(x) = Cnx" + Cn-1x"-1 +...+ co, and then start doing the long division).
Transcribed Image Text:Let a EK and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is f(a). (Hint: name the coefficients of f, i.e. write f(x) = Cnx" + Cn-1x"-1 +...+ co, and then start doing the long division).
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