As a packaging engineer, you model the capacity of a shipping container using the cubic function $V(x) = x^3 - 125$. You need to verify if an inner dimension represented by $x - 5$ perfectly divides this volume. Arrange the steps in the correct order to recall and apply the Factor Theorem for this specific volume model.

A quality control engineer uses the function $f(x) = x^3 - 125$ to model the volume of a precision-cut component. According to the Factor Theorem, which value of $x$ should the engineer substitute into the function to determine if the dimension $x - 5$ is a mathematical factor of this volume model?

A logistics coordinator uses the function $f(x) = x^3 - 125$ to model the volume of a standardized shipping container. To verify if a smaller packing unit with dimension $x - 5$ is a mathematical factor of this volume using the Factor Theorem, the coordinator calculates $f(5)$. According to the theorem, what numerical value must $f(5)$ result in to confirm that $x - 5$ is a factor?

A design engineer uses the polynomial $f(x) = x^3 - 125$ to model the capacity of a precision component. To determine if the dimension $x - 5$ is a factor of this model, the engineer applies the Factor Theorem. Match each component of the mathematical evaluation with its correct value or conclusion.

A fabrication specialist uses the polynomial $f(x) = x^3 - 125$ to model the volume of a precision-cut metal block. According to the Factor Theorem, if the specialist evaluates the function at $x = 5$ and determines that $f(5) = 0$, then the expression $x - 5$ is a factor of the volume function.

Recalling the Factor Theorem for Container Design

Verifying Container Dimensions with the Factor Theorem