A manufacturing technician is calculating the cost-per-unit for a batch of precision parts. The total cost is represented by $(x^3 - 64)$ and the number of units produced is $(x - 4)$. What is the correct simplified expression (quotient) for the cost-per-unit?

An inventory analyst at a distribution center is using the polynomial expression $(x^3 - 64) \div (x - 4)$ to model the density of items stored in a cubic bin relative to its side length. Arrange the following steps of the polynomial long division in the correct order to find the simplified density formula.

An inventory analyst at a distribution center is simplifying a volume-to-dimension ratio represented by the expression $(x^3 - 64) \div (x - 4)$. True or False: To perform polynomial long division correctly, the analyst must rewrite the dividend as $x^3 + 0x^2 + 0x - 64$ to include placeholders for the missing degrees.

A quality assurance technician is simplifying an efficiency ratio for an industrial cooling system. The total efficiency factor is represented by $x^3 - 64$ and the number of cooling cycles is $x - 4$. To correctly document the process, match each component of the polynomial long division to its corresponding mathematical expression.

Simplifying an Allocation Formula

Documenting Polynomial Division for Material Density

An inventory analyst at a distribution center is calculating the cross-sectional area of a storage bin. The total volume of the bin is represented by the expression $x^3 - 64$ cubic feet, and the height of the bin is represented by $x - 4$ feet. To find the area, the analyst divides the volume by the height: $(x^3 - 64) \div (x - 4)$. After correctly performing the division, the analyst obtains a simplified expression for the area in the form $x^2 + Bx + 16$. What is the numerical value of the missing coefficient $B$?