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The polynomial 2r + 1 has a multiplicative inverse in Z[x] oquals to: b) 1+2r d) None b)

The polynomial 2r + 1 has a multiplicative inverse in Z[x] oquals to: b) 1+2r d) None b)

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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part 9 10
Let f(x) - x' + 2x + 4 and g(x) - 3x + 2 in Z,x]. Then, upon dividing f(x) by g(x), we get 7- The quotient polynomial is: a) 1+ 2x + 2x. b) 2-2 27 c) 2+ 3x + 2x². d) None. O a) O b) O c) O d) 8- The remainder polynomial is: a) b) 8. c) 0. d) 2. O a) O b) O c) 9. The polynomial 2x + 1 has a multiplicative inverse in Z[x] equals to: a) b) 1+ 2x c)x +1 d) None O a) O b) 10-If p is a prime number, then in Z[x] the polynomial x P -1 – 1 = a) (x- 1) (x + 2) (x - 3)... (x+ p- 1). b) (x - 1) (r - 1) (x² – 1)... (x"- – 1). c) (x- 1) (r 2) (x- 3)... (x- p+1). d) (x- 1) (r- 2) (x – 3)... (x -p-1). O b) O c) O d)
Transcribed Image Text:Let f(x) - x' + 2x + 4 and g(x) - 3x + 2 in Z,x]. Then, upon dividing f(x) by g(x), we get 7- The quotient polynomial is: a) 1+ 2x + 2x. b) 2-2 27 c) 2+ 3x + 2x². d) None. O a) O b) O c) O d) 8- The remainder polynomial is: a) b) 8. c) 0. d) 2. O a) O b) O c) 9. The polynomial 2x + 1 has a multiplicative inverse in Z[x] equals to: a) b) 1+ 2x c)x +1 d) None O a) O b) 10-If p is a prime number, then in Z[x] the polynomial x P -1 – 1 = a) (x- 1) (x + 2) (x - 3)... (x+ p- 1). b) (x - 1) (r - 1) (x² – 1)... (x"- – 1). c) (x- 1) (r 2) (x- 3)... (x- p+1). d) (x- 1) (r- 2) (x – 3)... (x -p-1). O b) O c) O d)
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