To determine if $x - 4$ is a factor of the polynomial function $f(x) = x^3 - 64$ using the Factor Theorem, evaluate the function at the corresponding value of $c$. The theorem states that $x - c$ is a factor if and only if $f(c) = 0$. For the binomial $x - 4$, the value is $c = 4$. Substitute $x = 4$ into the function: $f(4) = 4^3 - 64$. Simplify the exponent to obtain $f(4) = 64 - 64$, which results in $f(4) = 0$. Since $f(4) = 0$, the Factor Theorem confirms that $x - 4$ is a factor of $f(x) = x^3 - 64$.