Question 1007704
I do not know what the diagonal test is, but this is the answer:

{{{ 6x^(2) y z^(2) + 3y + 6x y^(2) + 3x z^(2) = (6x^(2) y z^(2) + 3x z^(2)) + (3y + 6x y^(2)) = ( 3x z^(2) ) (2xy + 1) + 3y( 2xy + 1) = (2xy+1)(3xz^(2) + 3y) }}}