As a data analyst reviewing a predictive model's source code, you encounter the polynomial expression ${}3x^5y - 48xy$. To optimize the algorithm's performance, you need to recognize and input its completely factored form. Which of the following represents the completely factored form of this expression?

As a junior technical analyst for a manufacturing firm, you are documenting the optimization of a stress-test formula that uses the polynomial expression ${}3x^5y - 48xy$. To ensure the documentation is accurate, place the following procedural steps in the correct order to factor the expression completely.

A logistics analyst is verifying a shipping cost formula that uses the expression ${}3x^5y - 48xy$. To begin factoring this expression completely, the first step is to extract the Greatest Common Factor (GCF). The GCF for this expression is ${}3xy$.

In a technical report for an engineering project, a technician documents the complete factorization of the expression ${}3x^5y - 48xy$ as ${}3xy(x - 2)(x + 2)(x^2 + 4)$. To ensure the documentation is technically accurate, match each component of this process with its correct mathematical classification.

Structural Component Analysis Documentation

Load-Forecasting Model Factoring Documentation

A data analyst is reviewing the logic of a predictive model that uses the polynomial expression ${}3x^5y - 48xy$. To simplify the model's calculations, the expression must be completely factored. The analyst successfully factors out the Greatest Common Factor (GCF) of ${}3xy$ and identifies the linear binomial factors as $(x - 2)$ and $(x + 2)$. The final component of the completely factored form is an irreducible sum of squares, which is written as $x^2$ plus ____.