Application of Generalization of Eisenstein Criterion to Verify Irreducible Polynomial over Z[x] using MATLAB GUI

Abstract

Technology plays an important role in education development to prepare students to answer global challenges. Programming is one of the skills students need to have to adapt to advanced technology. Before preparing students for that skill, teachers need to be experts in programming into the subject they teach. Polynomial is a compulsory course for a master’s degree in teaching mathematics. It prepares the master’s student about the concept of an irreducible over any field. Each polynomial in the field C with degree one is an irreducible polynomial, while an irreducible polynomial in R[x] is of degrees one and two. However, for every polynomial in the field Q of degree n in Z, there is any irreducible polynomial, so it is hard to decide whether the polynomial with any degree  is irreducible or not. This paper aims to develop the project application in teaching and learning Polynomial using MATLAB GUI will be presented to check the irreducibility of a polynomial over Q[x] by using theorem on the Generalization of the Eisenstein Criterion. This project application can be used by lecturers and students of universities, moreover, the algorithm and steps of making an application can be adjusted to make the other application in mathematics.