Notice that we cannot directly apply Eisenstein criterion to Prove that the polynomial 1+x+x2 +...+ xp-1 . where p is a prime number, is irreducible over the field of rational numbers.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 6E: Prove Corollary 8.18: A polynomial of positive degree over the field has at most distinct zeros...
icon
Related questions
Question

**Notice that we cannot directly apply Eisenstein criterion to

Prove that the polynomial 1+x+x2 +...+ xp-1 . where p is a prime number, is irreducible over the field of rational numbers.

Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage