Zeros of third-degree polynomial (poles of a transfer function)

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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,