I've some transfer function which have following denominator:
$$(a_{2}c_{3}s+1)(a_{1}c_{1}c_{2}b_{1}s^{3}+b_{1}c_{2}s^{2}+a_{1}(c_{1}+c_{2})s+1).$$
I reduced part of the equation which is defined by third-degree polynomial. Now I have:
$$(a_{2}c_{3}s+1)(b_{1}c_{2}s^{2}+1)(a_{1}c_{2}s+1)+a_{1}c_{2}s.$$
I'm confused what to do with (or how to interpret) the $a_{1}c_{2}s$. As it is know, the poles of transfer function are described in denominator in form:
$$F(s) = \frac{...}{(s_{1}+1)(s_2+1)(s_3+1)...(s_n+1)}.$$
I know how to find first three poles, but I don't have any idea how can I modify the equation or interpret this "free part" ($a_{1}c_{2}s$)?
Regards,