3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists polynomials g(T) and h(T) in R[T], which are both not constant, i.e. of degree > 1, such that f(T) = g(T) · h(T).
3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists polynomials g(T) and h(T) in R[T], which are both not constant, i.e. of degree > 1, such that f(T) = g(T) · h(T).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...
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![3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists
polynomials g(T) and h(T) in R[T], which are both not constant, i.e. of
degree > 1, such that
f(T) = g(T) - h(T).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fbbb112-1902-4490-9475-b2c99ad6e439%2F056efa5e-fb03-487d-9420-2b477b8b474a%2F3p0vf8i_processed.png&w=3840&q=75)
Transcribed Image Text:3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists
polynomials g(T) and h(T) in R[T], which are both not constant, i.e. of
degree > 1, such that
f(T) = g(T) - h(T).
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