A small business owner uses the polynomial expression $-7a^3 + 21a^2 - 14a$ to model the fluctuating costs of raw materials, where $a$ represents the volume of production. To simplify the cost formula, the owner needs to factor the expression using its greatest common factor (GCF). Following the standard convention for expressions with a negative leading coefficient, what is the correctly factored form?

An operations manager is simplifying a supply chain model represented by the expression $-7a^3 + 21a^2 - 14a$. According to standard factoring conventions, the manager should factor out a positive greatest common factor (GCF) of ${}7a$.

An operations manager is simplifying a cost-efficiency model represented by the expression $-7a^3 + 21a^2 - 14a$. According to the standard algebraic convention for expressions with a negative leading coefficient, the manager must factor out the greatest common factor (GCF). The GCF for this expression is ____.

A warehouse manager is simplifying a formula that models inventory depreciation, represented by the expression $-7a^3 + 21a^2 - 14a$, where $a$ represents the age of the items in months. To simplify their records, they must factor the expression using its greatest common factor (GCF). Arrange the following steps in the correct order to complete the factoring process according to standard algebraic conventions.

A retail analyst uses the polynomial expression $-7a^3 + 21a^2 - 14a$ to model the rate of change in store foot traffic over several months. To simplify the model for a presentation, they must identify the specific components of the factoring process. Match each mathematical term with its correct expression or part of the process.