You are a logistics coordinator participating in a professional development course on data modeling. The course explains how algebraic formulas represent supply chain costs. Your instructor mentions that a formula's underlying polynomial needs to be 'completely factored' to easily identify key cost variables. What is the definition of a completely factored polynomial?

In a professional training module on algebraic modeling, you learn that a polynomial is considered completely factored if at least one of its polynomial factors (excluding monomial factors) can still be broken down into simpler polynomial products.

Standards for Algebraic Model Documentation

In your role as a logistics data analyst, you are documenting the cost-modeling formulas used in the company's optimization software. To ensure the technical manual is accurate, match each algebraic term below with the correct description of its role in ensuring a polynomial is 'completely factored.'

In your role as a technical documentation specialist for an engineering firm, you are updating the company's standards for mathematical modeling. According to these standards, a polynomial is considered completely factored when, after the greatest common factor has been extracted, all of its remaining factors (excluding any monomial factors) are __________ polynomials.