Algebra > Expressions > Factorising Quadratics
Generate a GCSE factorising quadratics worksheet focused on rewriting monic quadratics of the form x^2 + bx + c as two brackets. This reviewed generator includes prior knowledge, selectable worked-example types, fluency practice, interpretation questions, exam-style questions, answers and optional worked solutions.
Key ideas
Students need to recognise when a monic quadratic can be written as a product of two brackets.
For monic quadratics, the two numbers must multiply to the constant term and add to the coefficient of x.
This topic focuses on x^2 + bx + c. Harder non-monic quadratics are better treated as a later extension.
Factorising should be connected to expansion so students can check their answer.
Common mistakes
Choosing two numbers that multiply correctly but do not add correctly.
Dropping the x terms when moving from brackets back to the quadratic.
Assuming every quadratic factorises neatly over the integers.
Not checking by expanding the brackets.
Teaching notes
Start with expansion checks so students see factorising as reversing a structure.
Use minimally different examples to expose why both the sum and product matter.
Ask students to explain why a proposed factorisation cannot be right before correcting it.
Use the rectangle interpretation questions to connect factorising with area, not just algebraic manipulation.
Starter ideas
Find two numbers that multiply to 24 and add to 10.
Expand (x + 3)(x + 5). What would the reverse question be?
Which one does not belong: x^2 + 5x + 6, x^2 + 6x + 5, x^2 + 7x + 10, x^2 + 8x + 15?
Worksheet generation
The worksheet generator can create support content, prior knowledge, worked examples, fluency practice, problem solving, exam-style questions and answers. This link opens the generator directly on this topic.
Open GCSE worksheet generatorTeacher questions
The generator can produce support notes, prior knowledge questions, worked examples, fluency practice, standard practice, problem solving, exam-style questions, challenge questions, answers and optional hints.
This topic focuses on monic quadratics of the form x^2 + bx + c, where students choose two numbers that multiply to c and add to b.
Yes. The worksheet generator supports printing, PDF download through the browser print dialog, and Word export.
