Polynomial Factoring Worksheet Generator
The generator picks integer roots and reconstructs the trinomial, so each problem factors cleanly into linear factors over the integers. The hard setting throws in difference-of-squares (a²x² − b²) and perfect-square trinomials, which are worth recognising by pattern.
Frequently asked questions
What does 'monic' mean?
A monic polynomial has leading coefficient 1. Easy sticks to monic trinomials; medium uses a leading coefficient between 2 and 4.
Can the answers be checked by expansion?
Yes. Multiply the factored form back out and you should recover the original trinomial — a good way to self-check.
Why include difference of squares on hard?
It is one of the most recognisable factoring patterns: a²x² − b² = (ax − b)(ax + b). Drilling the pattern speeds up later work.