If $\mathit{P}\left(\mathit{x}\right)=\mathrm{(c)*3.0}{\mathit{x}}^3\mathrm{((p)*(m))*2.0(c)*2.0}{\mathit{x}}^2\mathrm{((p)*(m))*1.0(c)*1.0}\mathit{x}\mathrm{((p)*(m))*0.0(c)*0.0}$, P((r)*2.0) = 0  so $\left(\mathit{x}\mathrm{(((F)*2.0)*(p))*(m)}\mathrm{((r)*2.0)*(a)}\right)$  is a factor.

The corresponding quadratic factor can be found using long division, synthetic division or the "have and need" method.

 $\mathrm{(c)*3.0}{\mathit{x}}^3\mathrm{((p)*(m))*2.0(c)*2.0}{\mathit{x}}^2\mathrm{((p)*(m))*1.0(c)*1.0}\mathit{x}\mathrm{((p)*(m))*0.0(c)*0.0}$

= $\left(\mathit{x}\mathrm{(((F)*2.0)*(p))*(m)}\mathrm{((r)*2.0)*(a)}\right)\left(\mathrm{((q)*(c))*2.0}{\mathit{x}}^2\mathrm{(((q)*(p))*(m))*1.0}\mathrm{((((q)*(c))*1.0)*(r))*(a)}\mathit{x}\mathrm{(((q)*(p))*(m))*0.0}\mathrm{((((q)*(c))*(r))*0.0)*(a)}\right)$

$=\left(\mathit{x}\mathrm{(((F)*2.0)*(p))*(m)}\mathrm{((r)*2.0)*(a)}\right)\left(\mathrm{(a)*(d)}\mathit{x}\mathrm{(((F)*1.0)*(p))*(m)}\mathrm{(b)*(a)}\right)\left(\mathit{x}\mathrm{(((F)*3.0)*(p))*(m)}\mathrm{((r)*3.0)*(a)}\right)$

Note: P(((r)*1.0)*(d)) = 0 and P((r)*3.0) = 0  so we could have begun the factoring process with the factor ((a)*(d)x (((F)*1.0)*(p))*(m) (b)*(a)) or (x (((F)*3.0)*(p))*(m) ((r)*3.0)*(a)).