A manufacturing company uses the polynomial ${}500p^3 + 4q^3$ to model the structural load on a bridge. To perform a safety analysis, a technician must recall the components of the factored form. Match each part of the factoring process to its corresponding mathematical value or expression.

A warehouse manager uses the polynomial ${}500p^3 + 4q^3$ to represent the combined storage capacity of two different bin types. To simplify this for a database entry, the manager first factors out the Greatest Common Factor (GCF) of 4. Which of the following correctly identifies the values for $a$ and $b$ that should be used in the sum of cubes pattern $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ to factor the remaining expression?

A logistical engineer is verifying a mathematical model that uses the polynomial ${}500p^3 + 4q^3$ to represent container volumes. True or False: In the fully factored form of this polynomial, the middle term of the resulting trinomial factor is ${}5pq$.

A technical analyst at a manufacturing plant uses the expression ${}500p^3 + 4q^3$ to calculate the combined volume of two different storage units. To simplify the mathematical model for a report, the analyst must factor the expression completely. Arrange the following steps of the factoring process in the correct order from start to finish.

Industrial Energy Consumption Model