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Let f (x) and g (x) be two non-zero polynomials in R [x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + 8 (x)) < max (deg f (x), deg g (x)). (ii) If f (x) g (x) #0, then deg (f (x) g (x)) < deg ƒ (x) + deg g (x). (iii) If R is an integral domain, then deg (f (x) g (x)) = deg f (x) + deg g (x). %3D

Let f (x) and g (x) be two non-zero polynomials in R [x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + 8 (x)) < max (deg f (x), deg g (x)). (ii) If f (x) g (x) #0, then deg (f (x) g (x)) < deg ƒ (x) + deg g (x). (iii) If R is an integral domain, then deg (f (x) g (x)) = deg f (x) + deg g (x). %3D

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 f(x) and g (x) be two non-zero polynomials in R[x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + g (x)) < max (degf (x), deg g (x)). (ii) If f (x) g (x) # 0, then deg (f (x) g (x)) < degf (x) + deg g (x). (iii) If R is an integral domain, then deg (f (x) g (x)) = deg f (x) + deg g (x). %3D
Transcribed Image Text:Let f(x) and g (x) be two non-zero polynomials in R[x], R being any ring. (i) If f (x) + g (x) # 0, then deg (f (x) + g (x)) < max (degf (x), deg g (x)). (ii) If f (x) g (x) # 0, then deg (f (x) g (x)) < degf (x) + deg g (x). (iii) If R is an integral domain, then deg (f (x) g (x)) = deg f (x) + deg g (x). %3D
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