Knowledge Organiser: Factorising
Part of Factorising · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Factorising within Factorising for GCSE Mathematics. Revise Factorising in Algebra for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 13 of 13 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 13 of 13
Practice
12 questions
Recall
3 flashcards
Knowledge Organiser: Factorising
Key Terms
- Factorise: Write an expression as a product of its factors
- HCF: Highest Common Factor — the largest factor shared by all terms
- Factor: A number or expression that divides exactly into another
- Quadratic: An expression with a highest power of x² (e.g. x² + 5x + 6)
- Difference of two squares: a² − b² = (a + b)(a − b)
Must-Know Facts
- Factorising is the reverse of expanding brackets
- Always look for a common factor first
- For x² + bx + c: find two numbers that multiply to c and add to b
- If signs are both +: both bracket signs are + (e.g. x² + 7x + 12)
- If the last sign is −: one bracket is +, one is − (e.g. x² + x − 12)
- If both signs are −: the larger factor is − (e.g. x² − 7x + 12 = (x−3)(x−4))
- Always check by expanding your answer
Key Formulas
- ab + ac = a(b + c)
- x² + (a+b)x + ab = (x + a)(x + b)
- a² − b² = (a + b)(a − b)
- For ax² + bx + c: find two numbers multiplying to ac and adding to b
Common Mistakes
- Incomplete factorisation: 4x² + 8x = 2x(2x + 4) — still factorisable; fully factorise to 4x(x + 2)
- Sign errors in quadratics: x² − 5x + 6 = (x − 2)(x − 3) — both negative; check by expanding
- Difference of two squares: x² − 9 = (x + 3)(x − 3), not (x − 3)²
- ax² + bx + c (a ≠ 1): Must find two numbers multiplying to ac (not c) and adding to b
- Confusing factorising with solving: Factorising gives brackets; set each bracket = 0 only when solving
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Practice Questions for Factorising
Which is the correct factorisation of 6x + 15?
A student factorises x² + 5x + 4 as (x + 4)(x + 4). Explain why this is incorrect and give the correct factorisation.
Quick Recall Flashcards
12 questions on Factorising — practise free
Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.
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