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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).

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).

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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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).
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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