I have the function $$ P(x)=\frac{\frac{l^2\beta}{6v^2}x^2+\frac{2l^2\beta^2}{6v^2}x+\beta}{\frac{l^2}{6v^2}x^3+\left(\frac{l^2\beta}{2v^2}+\frac{l}{2v}\right)x^2+\left(\frac{l^2\beta^2}{3v^2}+1+\frac{l\beta}{v}\right)x+\beta+\frac{v}{l}} $$ which I need to write as $$ P(x)=C\frac{(x-z_1)(x-z_2)}{(x-p_1)(x-p_2)(x-p_3)}. $$
I've already found the zeros, $z_{1,2}=-\beta\pm\sqrt{\beta^2-\frac{6v^2}{l^2}}$, but I'm having trouble finding the poles. I've tried Wolfram Mathematica but it solves it using $v$ as the variable. I've also tried this method (creating a system of equations) but my function is too complicated. I'm pretty sure $C=\frac{v^2}{l^2}$ because factoring it out simplifies the denominator quite a bit. Any help is appreciated.