A technician is using the Factor Theorem to verify if $x - 4$ is a factor of a design function $f(x) = x^3 - 64$. To confirm $x - 4$ is a factor, the technician must show that $f(4)$ is equal to which value?

An industrial engineer is evaluating the polynomial function $f(x) = x^3 - 64$, which represents the volume tolerances of a shipping container. According to the Factor Theorem, the engineer can confirm that $x - 4$ is a factor of this function because evaluating $f(4)$ yields a result of zero.

In a manufacturing design process, an engineer uses the Factor Theorem to determine if a specific dimension $x - 4$ is a factor of the volume function $f(x) = x^3 - 64$. Match each component of this verification process with its correct description.

A logistics coordinator is evaluating a storage container's volume function $f(x) = x^3 - 64$. To verify if a specific dimension $x - 4$ is a factor of this function, the coordinator follows a standard verification procedure. Arrange the steps of this process in the correct order.

Shipping Container Volume Analysis

An industrial designer is modeling a new shipping container's dimensional limits using the polynomial function $f(x) = x^3 - 64$. To check if the length adjustment $x - 4$ is a perfect factor of the volume function using the Factor Theorem, the designer must identify the correct value of $c$ in the divisor $x - c$ to substitute into the function. To perform this verification, the designer must evaluate the polynomial at $x =$ ____.

Factor Theorem Verification in Quality Control