Evaluating $(f \cdot g)(2)$ for $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$

An inventory analyst is modeling the total storage space required for new products. The number of product batches is given by $f(x) = x + 2$, and the volume per batch is modeled by $g(x) = x^2 - 3x - 4$. To find the total volume function $(f \cdot g)(x)$, the analyst needs to multiply these polynomials. Arrange the steps of this multiplication process in the correct order.

An inventory manager is modeling the total storage capacity of a warehouse. The number of storage racks is represented by the function $f(x) = x + 2$ and the items per rack is modeled by $g(x) = x^2 - 3x - 4$. Which of the following simplified polynomials represents the correct product function $(f \cdot g)(x)$ for the total items in the warehouse?

A retail supervisor is modeling total inventory by multiplying the function for the number of incoming orders, $f(x) = x + 2$, by the function for the number of items per order, $g(x) = x^2 - 3x - 4$. True or False: The simplified product function representing the total number of items, $(f \cdot g)(x)$, is $x^3 - x^2 - 10x - 8$.

A business analyst is modeling total projected revenue. The number of active service contracts is given by $f(x) = x + 2$, and the average revenue per contract is $g(x) = x^2 - 3x - 4$, where $x$ represents the expansion scale. Match each stage of the multiplication process for the total revenue function $(f \cdot g)(x)$ with its corresponding algebraic expression.

Logistics Inventory Modeling

Polynomial Multiplication Procedure in Cost Modeling

A logistics specialist is modeling a warehouse's total storage capacity. The number of active storage racks is represented by $f(x) = x + 2$, and the average number of items stored per rack is modeled by $g(x) = x^2 - 3x - 4$. To find the total storage capacity function, $(f \cdot g)(x)$, the specialist multiplies these polynomial functions, expanding the expression to $x^3 - 3x^2 - 4x + 2x^2 - 6x - 8$.

When the specialist combines the like terms to write the final simplified product function in the form $x^3 - x^2 + Bx - 8$, the value of the coefficient $B$ is ____.