Consider the function y= ax + bx+C, where a is in the set {n EN(n|15)}, b is a natural number less than 10, and c is a prime less than 20. How many second degree polynomials can we make in the form yexX&, where a,b, and c are in the given sets? (Input a single number for your answer, no punctuation, no spaces.)

Consider the function y= ax + bx+C, where a is in the set {n EN(n|15)}, b is a natural number less than 10, and c is a prime less than 20. How many second degree polynomials can we make in the form yexX&, where a,b, and c are in the given sets? (Input a single number for your answer, no punctuation, no spaces.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 5E: 5. Decide whether each of the following subset is a subring of , and justify your decision in each...

See similar textbooks

Similar questions

5. Decide whether each of the following subset is a subring of , and justify your decision in each case. a. The set of all polynomials with zero constant term. b. The set of all polynomials that have zero coefficients for all even powers of . c. The set of all polynomials that have zero coefficients for all odd powers of . d. The set consisting of the zero polynomials together with all polynomials that have degree 2 or less.
a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant polynomial in Z3[ x ], if one exists, that is a unit. c. Prove or disprove that there exist nonconstant polynomials in Zp[ x ] that are units if p is prime.
11. a. List all the polynomials in that have degree 2. b. Determine which of the polynomials in part a are units. If none exists, state so.
When we divide a polynomial P(x) by a divisor D(x), the Division Algorithm tells us that we can always obtain a quotient Q(x) and a remainder R(x). State two forms in which the result of this division can be written.