Well, the denominator is a polynomial of degree three. I'll assume that $f(x)$ is a polynomial of degree $\leq 2$. Actually, the case $f(x)=1$ already explains the philosophy.
The numerator of the first fraction will be multiplied by a linear polynomial, so that its degree must be one, if you hope to compete with the second fraction. Assume that
and you definitely need a term like $x^2$ on the right-hand side to cancel $Cpx^2$. That's why you need at least a polynomial $E(x)$ of the first order.