Factorize Parametric Polynomials

Question

Is there a possibility to factorize a parametric polynomial expression - meaning that the coefficients are defined as parameters, and not as specific numbers?

My example - a polynomial in s, with R1, ..., R5 and C1, ..., C2 being parameters:

LP2nTfDen = R1 R4 + R4 R5 + C2 R1 R2 R4 s + C1 R1 R3 R5 s + C2 R2 R4 R5 s -
            C1 C2 R1 R2 R4 R5 s^2

I'd like Mathematica to transform the expression in the form (A + s) (B + s) ..., A, B, etc. being expressions of R1, ..., R5, C1, C2. Is this possible?

Answer 1

It looks like your resulting expression will have a unit coefficient for the highest power. In this case you can do :

expr = Times @@ (s - Solve[LP2nTfDen/Last@CoefficientList[LP2nTfDen, {s}] == 0, s][[All,1, 2]]) ;

expr == LP2nTfDen/Last@CoefficientList[LP2nTfDen, {s}] // Simplify

(* True *)