Evaluating $(f \cdot g)(2)$ for $f(x) = x - 7$ and $g(x) = x^2 + 8x + 4$

A business analyst is modeling a company's total revenue function, $(f \cdot g)(x)$, where $x$ represents the number of units sold. If the growth factor is represented by $f(x) = x - 7$ and the revenue-per-unit is represented by $g(x) = x^2 + 8x + 4$, which of the following is the correct simplified expression for the total revenue function?

A supply chain analyst is determining a projected cost model by calculating $(f \cdot g)(x)$ where the baseline adjustment is $f(x) = x - 7$ and the variable rate is $g(x) = x^2 + 8x + 4$. Arrange the standard procedural steps required to recall and execute this polynomial multiplication from start to finish.

A financial analyst is developing a cost model using the functions $f(x) = x - 7$ and $g(x) = x^2 + 8x + 4$. The analyst determines that the simplified product function $(f \cdot g)(x)$, which represents the total projected cost, is $x^3 + x^2 - 52x - 28$. Is the analyst's determination correct?

A logistics analyst is modeling the total performance of a distribution center using the product function $(f \cdot g)(x)$, where $f(x) = x - 7$ represents the shift duration factor and $g(x) = x^2 + 8x + 4$ represents the throughput rate. Based on the standard procedure for multiplying these polynomials, match each part of the calculation with its corresponding mathematical expression.

Manufacturing Cost Model Optimization

Documenting the Total Cost Function Computation

An inventory analyst is modeling the total storage costs of a warehouse using the product function $(f \cdot g)(x)$, where the adjusted quantity factor is $f(x) = x - 7$ and the storage fee rate is $g(x) = x^2 + 8x + 4$. After distributing the terms, the unsimplified product is $x^3 + 8x^2 + 4x - 7x^2 - 56x - 28$. When the analyst simplifies this expression by combining the like linear terms, the coefficient of the linear term, $x$, in the final product function $(f \cdot g)(x)$ is ____.