✏️ Factorising Quadratics

About Factorising Quadratics

Factorising is expanding run backwards, and pupils who can expand fluently often stall here because the search feels like guesswork. It is not: for a monic quadratic you need two numbers that multiply to the constant and add to the coefficient of x, and once that is framed as a search with two conditions rather than inspiration, it becomes systematic. Every quadratic on this worksheet is generated from its own factors rather than picked and then tested, which means a factorisation always exists — a pupil never spends five minutes on a question that has no integer answer. The check runs the other way too: each generated answer is expanded again and compared against the printed polynomial before the question is accepted, so the key cannot drift from the question. The levels move through positive factor pairs, then larger pairs, then negative constants where the factors have opposite signs, then mixed signs throughout, and finally non-monic quadratics with a common factor that can be taken out first — the only non-monic form the method taught here handles cleanly. Twelve questions per page. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key. Its on-screen twin is Factorise Reverse Builder.

Common questions

Do all the quadratics actually factorise?

Yes. Each one is generated from its own factors, so a pupil never works on a question with no integer answer.

How is the answer key checked?

Each answer is expanded again and compared against the printed polynomial before the question is accepted.

Are non-monic quadratics included?

At the highest level only, and only with a common factor that can be taken out first — the form the taught method handles cleanly.

Is an answer key included?

Yes. Every level downloads with its own separate answer key PDF.