A design team uses the polynomial expression ${}8x^3y - 10x^2y^2 + 12xy^3$ to represent the total area of three distinct workspace zones. To simplify their architectural blueprints, they must first identify the Greatest Common Factor (GCF) of the three terms. What is the GCF of this expression?

A warehouse logistics analyst uses the polynomial expression ${}8x^3y - 10x^2y^2 + 12xy^3$ to represent the volume distribution of three storage zones. To simplify the tracking database, the analyst needs to factor this expression by extracting the Greatest Common Factor (GCF). Arrange the following steps in the correct chronological order to complete the factoring process.

A logistics manager uses the expression ${}8x^3y - 10x^2y^2 + 12xy^3$ to represent the total volume of three distinct storage zones. To simplify the inventory database, the manager must factor out the Greatest Common Factor (GCF). The manager determines that the GCF for the variable $x$ should be $x^3$ because it is the highest power of $x$ present in the terms. Is this reasoning correct?

A production supervisor uses the polynomial expression ${}8x^3y - 10x^2y^2 + 12xy^3$ to track the raw material requirements for three different manufacturing shifts. To simplify the tracking sheet, the supervisor factors out the Greatest Common Factor (GCF), which is identified as ${}2xy$. Match each original term from the expression with the factor that remains after the GCF ${}2xy$ is factored out.

An inventory analyst is simplifying a storage capacity formula represented by the polynomial ${}8x^3y - 10x^2y^2 + 12xy^3$. When determining the Greatest Common Factor (GCF) for the variables $x$ and $y$, the analyst must recall the standard factoring rule: for any shared variable, always extract the ____ power of that variable present in all terms.