> I believe it still may be possible to find these unknown polynomial factors by migrating some of the polynomial terms through redistribution of higher value t

> I believe it still may be possible to find these unknown polynomial factors by migrating some of the polynomial terms through redistribution of higher value terms and/or performing some sort of hard search. You start with a fairly obvious representation of the integer as a polynomial. If that doesn't give you some sort of factorisation, then any information that allows you a better guess at a factorable polynomial is also information that helps you outright factor the original number.