Suppose $f$  is a rational function with polynomial functions $p(x)$ and $q(x)$ so that for any $x \in D_f$, it domain, with $q(x) \ne 0$, $f(x) = \frac {p(x)} {q(x)}$.

Definition: The factored form of $R$ is
$R(x) = \frac {P(x)} {Q(x)} =\frac {A_P*P_1(x)*P_2(x)*...*P_m(x)*g_P(x)} {A_Q*Q_1(x)*Q_2(x)*...*Q_n(x)*g_Q(x)}$ .

where $P_j(x) =(x- r_j)^{p_j}$,  for $j = 1,2, ... , m$, $Q_i(x) =(x- s_i)^{q_i}$,  for $i = 1,2, ... , n$, and  $g_P$ and  $g_Q$ are monic polynomials with no real roots.