Question 879815
Rather use discriminant to avoid testing different combinations.

{{{ax^2+bx+c}}} has a discriminant number, {{{b^2-4ac}}}.  If discriminant is a  square integer, then the quadratic trinomial is factorable.


3y^2+14y+4,
check {{{14^2-4*3*4=196-48=148}}}.
What happens if you form sqrt(148)?
{{{2*sqrt(37)}}}, irrational; so the roots of the polynomial are also irrational, so 3y^2+14y+4 is not factorable (unless you want irrational constants in your binomials).


9p^2-p+3p, assuming you made a misprint when you showed -q;
Check yourself...  discriminant, {{{(-1)^2-4*9*3}}}....