Um estudo introdutório sobre os polinômios palindrômicos

Abstract

This paper explores the study of complex numbers and palindromic polynomials, delving into their rich history, mathematical properties, and applications. The aim is to provide a comprehensive understanding of these topics, contributing to the field of mathematics education. The historical context of complex numbers is initially presented, tracing their development from conception to their establishment in mathematical theory. Some key milestones and historical contributions that led to the development of this field are discussed. Next, an analysis of palindromic polynomials is conducted, focusing on this special class of polynomials that exhibit symmetry with respect to their vertical axis. The properties and characteristics of these polynomials are explored, including the relationship between their roots and the symmetry of their coefficients. A notable highlight of this work is the introduction of an alternative method for reducing the degree of palindromic polynomials with real coefficients. This innovative method offers a fresh approach to addressing this problem, providing a new perspective on manipulating palindromic polynomials. To facilitate understanding of the concepts and operations discussed, the software GeoGebra is utilized, enabling visualizations and interactive exploration of these topics. GeoGebra serves as a valuable tool, providing visual illustrations and practical examples of the operations and concepts covered. In conclusion, this study offers an in-depth approach to complex numbers and palindromic polynomials, providing a deeper understanding of these topics. It contributes to the field of mathematics education, offering a valuable resource for students and teachers interested in exploring these concepts more comprehensivel.