A facilities coordinator is organizing office space and needs to simplify the expression xy + 3y + 2x + 6, which represents the total square footage of two adjacent suites. Arrange the following steps in the correct order to factor this expression using the grouping method.

A project manager is using the polynomial expression xy + 3y + 2x + 6 to determine the total resource allocation for a two-phase project. According to the grouping method, which of the following is the correctly factored form of this expression?

A facilities manager is simplifying a floor plan area represented by the polynomial expression $xy + 3y + 2x + 6$. To factor this by grouping, the manager first extracts common factors from two pairs of terms, resulting in the intermediate form: $y(x + 3) + 2(x + 3)$. According to the grouping method, identify the common binomial factor shared by both terms in this expression: ____.

An office facility manager is simplifying a square footage calculation represented by the polynomial expression $xy + 3y + 2x + 6$. To factor this expression by grouping, the manager must identify the correct mathematical components for each stage of the process. Match each term below with its correct functional role in the factoring steps.

A warehouse coordinator is organizing storage sections where the total floor space is represented by the expression $xy + 3y + 2x + 6$. To factor this expression by grouping, the coordinator first pairs the terms as $(xy + 3y) + (2x + 6)$. True or False: According to the grouping method, the greatest common factor (GCF) of the first group, $(xy + 3y)$, is $y$.

Rationale for Selecting the Grouping Method

Documenting Factoring Steps for Workspace Analysis

Office Space Partitioning

A production supervisor is calculating the total output for two manufacturing shifts using the polynomial expression $xy + 3y + 2x + 6$. To factor this expression by grouping, the supervisor first organizes the terms into two pairs: $(xy + 3y) + (2x + 6)$. According to the grouping method, what is the greatest common factor (GCF) of the second group, $(2x + 6)$?

A project coordinator is verifying a simplified resource model derived from the original expression $xy + 3y + 2x + 6$. After factoring the expression into $(x + 3)(y + 2)$, the coordinator performs the final step of the grouping method: 'Check by multiplying.' According to the standard procedure, what is the primary purpose of this final step?