# Nearly irreducibility of polynomials and the Newton diagrams

## TL;DR

This paper introduces a criterion based on Newton diagrams to determine when a polynomial in two complex variables is nearly irreducible, meaning its factors share a common zero.

## Contribution

It provides a novel criterion for nearly irreducibility of polynomials using Newton diagrams, linking geometric and algebraic properties.

## Key findings

- Criterion for nearly irreducibility based on Newton diagrams
- Characterization of polynomial factors sharing common zeros
- Connection between geometric diagrams and algebraic factorization

## Abstract

Let f be a polynomial in two complex variables. We say that f is nearly irreducible if any two nonconstant polynomial factors of f have a common zero. In the paper we give a criterion of nearly irreducibility for a given polynomial f in terms of its Newton diagram.

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Source: https://tomesphere.com/paper/1905.02288