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We won't be able to answer this accurately without knowing the polynomials.
Other polynomials of the same, or lower, order.
Reducible polynomials.
Whenever there are polynomials of the form aX2+bX+c=0 then this type of equation is know as a quadratic equation. to solve these we usually break b into two parts such that there product is equal to a*c and I hope you know how to factor polynomials.
Yes.