The Factor Theorem connects the factors of a polynomial function to its function values. It states that for any polynomial function $f(x)$: if $x - c$ is a factor of $f(x)$, then the function evaluated at $c$ equals zero ($f(c) = 0$). The reverse is also true: if evaluating the function at $c$ results in zero ($f(c) = 0$), then $x - c$ is a factor of the polynomial function $f(x)$. This theorem implies that a divisor $x - c$ is a factor of $f(x)$ whenever the division results in a remainder of zero.