Let $q(y, z) = u_1 + u_2y + u_3 z + u_4y^2 + u_5yz + u_6z^2 + u_7y^3 + u_8y^2z + u_9yz^2 +$ $\hspace{2.55cm}u_{10}y^3z + u_{11}y^2z^2 + u_{12}y^3z^2$

Can $q(y, z)$ be factorized as \begin{equation} q(y, z) =(v_1+v_2y)(v_3+v_4y+v_5z+v_6yz)(v_7+v_8y+v_9z+v_{10}yz)? \end{equation}

Here, {$u$} and {$v$} are complex numbers.

Are there any general principles to factorize a bivariate polynomial?

Thanks.