Confusion regarding terminology
A rational number is a number that can be written as a fraction, a / b, where a and b are integers.    This is not a synonym of a transfer function yet all numbers used in such are rational because of truncation, rounding, fractions or integers.
Irrational numbers have decimal expansions that neither terminate nor become periodic but if a transfer function only has a limited number of significant figures due to tolerances, irrational numbers can be used but truncated to the number of &quot;sig figs&quot;.
Using an infinite series value in a transfer function would be not only irrational in the logical sense but also insignificant in the mathematical sense.
So they are not synonyms but commonly used together.

2nd Order filters are common in RLC filters and active filters and may be represented in a number of ways including Factored Form.
  REF
Higher order filters may be cascaded to create different responses by cascading LCLCLC or 2nd order Active filters.
e.g. 4th order Chebychev.  10kHz  Active and 50 Ohm passive
The transfer functions of filters are often made from 2nd order sections LC or their equivalent RC*(-RC) with negative feedback. But they can also be any odd order as well or any feasible length of polynomial order or slope of rolloff.
So they are not synonyms but it is common to convert a polynomial into factored numbers to visualize the pole locations of a filter or pole/zero transfer functions.