Factorisation
Factorising rewrites a sum as a product. Look for a common factor first, then decide whether the remaining expression fits a quadratic or a special identity. Expanding your factors checks that the expression has not changed.
What this guide covers
Common factors, grouping, quadratic expressions and difference of two squares. This guide focuses on factorisation, not the changing-the-subject portion of the same graph objective.
Syllabus reference: 2026 Mathematics 4052, N5, page 6. These are Mentora search groupings, not new official syllabus categories.
Worked example
Factorise 2x² − 10x + 12.
Take out 2: 2(x² − 5x + 6). Two numbers with product 6 and sum −5 are −2 and −3, so the result is 2(x − 2)(x − 3). Expanding gives 2x² − 10x + 12 again.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Factorise 15a − 25.
Show worked answer
The greatest common factor is 5, so 15a − 25 = 5(3a − 5).
Check 2
Factorise x² + x − 20.
Show worked answer
5 × (−4) = −20 and 5 + (−4) = 1, so (x + 5)(x − 4).
Check 3
Factorise 9y² − 16.
Show worked answer
This is a difference of squares: (3y − 4)(3y + 4). The middle terms cancel when expanded.
Common mistakes to watch for
- Factoring only one term changes the expression: divide every term by the extracted factor.
- A negative constant needs factors with opposite signs. Check both the product and the sum.
- Factorising an expression does not by itself give values of x. The zero-product rule applies when a product equals zero.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
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More G3 Math topicsPublished by Mentora · Sources checked 11 Sept 2026
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Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.