I repeatedly see two representations of the general transfer function in the literature. The first is the following which is factorization of the numerator and denominator polynomials:
$$\textbf{G}(s) = k \frac{ (s - a_{1})(s - a_{2})(s - a_{3})\ldots }{ (s - b_{1})(s - b_{2})(s - b_{3})(s - b_{4})\ldots }$$
The alternative, below, eludes me and I'll checked many sources but none seem to justify it. The difference is a lowly $s$ term in the denominator raised to a power. Is this general form related the open-loop transfer function?
$$\textbf{G}(s) = k \frac{ (s - a_{1})(s - a_{2})(s - a_{3})\ldots }{s^m (s - b_{1})(s - b_{2})(s - b_{3})(s - b_{4})\ldots }$$
My question is what is the difference, if any in these two forms?