A software developer is optimizing a calculation engine that processes the polynomial ${}15x^3y - 3x^2y^2 + 6xy^3$. To simplify the formula, the developer needs to extract the greatest common factor (GCF) from the three terms. What is the GCF of ${}15x^3y$, $-3x^2y^2$, and ${}6xy^3$?

A software engineer is refactoring an optimization algorithm that uses the polynomial ${}15x^3y - 3x^2y^2 + 6xy^3$. To simplify the code, the engineer identifies the greatest common factor (GCF) as ${}3xy$ and rewrites each term as a product. Match each original term of the polynomial with its equivalent form when expressed as a product of the GCF and its remaining factor.

A supply chain analyst is simplifying a storage capacity formula represented by the polynomial ${}15x^3y - 3x^2y^2 + 6xy^3$. True or False: By factoring out the greatest common factor (GCF) of ${}3xy$, the analyst can rewrite the expression in its factored form as ${}3xy(5x^2 - xy + 2y^2)$.

A business analyst is simplifying a revenue projection model represented by the polynomial ${}15x^3y - 3x^2y^2 + 6xy^3$. To optimize the formula, the analyst needs to factor out the greatest common factor (GCF). Arrange the following steps in the correct order to complete the factoring process according to the standard procedure.

Optimizing a Resource Allocation Algorithm

Streamlining a Logistics Script

A facilities planner at a regional distribution center is analyzing the floor space usage of three storage zones. The total volume of inventory, expressed in cubic meters, is represented by the multi-variable polynomial expression ${}15x^3y - 3x^2y^2 + 6xy^3$. To simplify the spatial allocation calculations, the planner wants to factor out the greatest common factor (GCF) from all three terms.

What is the greatest common factor (GCF) of the terms in this expression? (Type your answer in lowercase, without any spaces, e.g., 2ab): ____