代做数学Homework MAT401 Homework 4

MAT401 Homework 4

代做数学Homework Determine whether or not each of the following polynomials is irreducible over Q. Explain what method you used

Read: Gallian, Chapters 17 and 18 (Omit the material on Euclidean domains)

Problems:  代做数学Homework

These problems are due on Crowdmark by 6pm on Wednesday, February 16. The solutions will be discussed in tutorials that week.


  1. Consider polynomials in R = Z2[x] and recall that non-constant polynomials in this ring have a unique factorization into irreducibles. In homework 3 you found the irreducibles of degree at most 3.

(i) Find all irreducible polynomials of degree 4. Explain your answer. (There are 3 of them.)

(ii) Find the factorization into irreducibles of the following polynomials:

代做数学Homework


  1. Determine whether or not each of the following polynomials is irreducible over Q. Explain what method you used.  代做数学Homework

代做数学Homework


  1. Suppose that r is a non-zero real number such that the quantity r + 1/r is three times an integer. Show that r is irrational.

代做数学Homework

(ii) Show that the elements 2 and 1 + 5 are both irreducible inR.

(iii) Show that R is not a UFD.  代做数学Homework

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