All Abstract Algebra Resources
Example Questions
Example Question #3 : Abstract Algebra
What definition does the following correlate to?
If is a prime, then the following polynomial is irreducible over the field of rational numbers.
Possible Answers:
Ideals Theorem
Principal Ideal Domain
Eisenstein's Irreducibility Criterion
Primitive Field Theorem
Gauss's Lemma
Correct answer:
Eisenstein's Irreducibility Criterion
Explanation:
The Eisenstein's Irreducibility Criterion is the theorem for which the given statement is a corollary to.
The Eisenstein's Irreducibility Criterion is as follows.
is a polynomial with coefficients that are integers. If there is a prime number that satisfy the following,
Then over the field of rational numbers is said to be irreducible.
Melissa
Certified Tutor
Certified Tutor
Bates Technical College, Associate in Science, Nursing (RN). Sam Houston State University, Bachelor of Science, Nursing (RN).
Rhaiza
Certified Tutor
Certified Tutor
CUNY Hunter College, Bachelor of Science, Psychology. DeVry Institute of Technology, Associate, Business Information Systems.
All Abstract Algebra Resources
Popular Subjects
Math Tutors in San Francisco-Bay Area, Computer Science Tutors in San Diego, GRE Tutors in Los Angeles, English Tutors in Atlanta, SSAT Tutors in Dallas Fort Worth, LSAT Tutors in New York City, Statistics Tutors in Chicago, Algebra Tutors in Denver, Reading Tutors in Los Angeles, GRE Tutors in Chicago
Popular Courses & Classes
SAT Courses & Classes in Seattle, ACT Courses & Classes in San Diego, GRE Courses & Classes in San Diego, ISEE Courses & Classes in Chicago, SSAT Courses & Classes in San Diego, GMAT Courses & Classes in Miami, GRE Courses & Classes in Houston, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area
Popular Test Prep
SAT Test Prep in Houston, LSAT Test Prep in Miami, SSAT Test Prep in Boston, LSAT Test Prep in Seattle, GMAT Test Prep in Washington DC, MCAT Test Prep in New York City, GRE Test Prep in Seattle, ACT Test Prep in Los Angeles, ISEE Test Prep in Chicago, ACT Test Prep in Philadelphia
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)