When performing the polynomial long division of ${}125x^3 - 8$ by ${}5x - 2$, what is the first term of the resulting quotient?

An inventory manager is calculating the base area of a storage container where the total volume is ${}125x^3 - 8$ and the height is ${}5x - 2$. To find the area, the manager must divide the volume by the height. Arrange the following steps of the polynomial long division process in the correct order to complete the calculation.

A logistics technician is verifying the dimensions of a storage unit where the total volume is $({}125x^3 - 8)$ and the height is $({}5x - 2)$. To find the base area, the technician uses polynomial long division. Match each part of the division process with the corresponding mathematical expression or value produced.

A technical analyst is calculating a volume-to-area ratio using the polynomial division $(125x^3 - 8) \div (5x - 2)$. To ensure that the long division process is set up correctly, the analyst determines that the dividend must be rewritten with placeholders for the missing degrees as ${}125x^3 + 0x^2 + 0x - 8$. Is the analyst's determination true or false?

Algebraic Reference Manual Update

A fabrication technician at an aerospace manufacturing company is updating the equipment dimension manual. They must verify the base area of a cylindrical storage unit where the volume is represented by the polynomial expression $({}125x^3 - 8)$ cubic meters and the height is represented by $({}5x - 2)$ meters. Since the base area is calculated by dividing the volume by the height, the technician performs the polynomial long division $({}125x^3 - 8) \div ({}5x - 2)$ to find the simplified quadratic expression for the base area. The constant term in the resulting base area polynomial is ____.

Manufacturing Calculation Audit: Base Area Determination