A manufacturing company tracks the production costs for two different product lines using the expression $c(q + 10) + 5(q + 10)$, where $c$ represents the unit material cost and $q$ represents the quantity of items produced. In this combined cost expression, which binomial represents the greatest common factor (GCF)?

An inventory manager calculates the total cost of two product orders using the expression ${}45(p + 10) + x(p + 10)$, where $p$ is the base price and 10 is the shipping surcharge. In this expression, the binomial greatest common factor (GCF) is ____.

A warehouse manager uses the expression $R(h + 40) + 15(h + 40)$ to calculate total storage costs, where $h$ represents hours of operation. True or False: In this expression, the binomial $(h + 40)$ is the greatest common factor (GCF) shared by both terms.

Factoring Shared Labor and Benefit Costs

An operations manager is reviewing financial models for different departments. Each formula is structured with a common binomial factor representing a shared variable, such as a base rate or project duration. Match each total cost or revenue expression with its corresponding binomial greatest common factor (GCF).

A financial analyst is simplifying a formula used to calculate projected returns on two investment portfolios. The total projected return is represented by the expression ${}5t(t + 12) - 3(t + 12)$. To enter this into their modeling software efficiently, they must factor out the binomial greatest common factor (GCF). Arrange the steps they should recall and follow to factor this expression correctly.

Identifying Common Shared Costs in Facilities Management