Some factorization results on polynomials having integer coefficients

Abstract

In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials. Such classes of polynomials are devised by imposing some sufficiency conditions on their coefficients along with some conditions on the prime factorization of the constant term or the leading coefficient of the underlying polynomials in conjunction with the information about their root location.

KEYWORDS:

• Dumas irreducibility criterion
• Eisenstein’s irreducibility criterion
• Perron’s irreducibility criterion
• polynomial factorization

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 12E05
• 30C15
• 11C08
• 26C10
• 26D05
• 30A10

Acknowledgments

The authors are indebted to the anonymous referee for valuable suggestions in improving the article.

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

The present research is supported by Science and Engineering Research Board (SERB), a statutory body of Department of Science and Technology (DST), Government of India through the project Grant No. MTR/2017/000575 awarded to the first author under the MATRICS Scheme. The financial support from the Council of Scientific and Industrial Research to the second author in the form of Junior Research Fellowship wide Grant No. CSIRAWARD/JRF-NET2022/11769 is gratefully acknowledged.