Singapore Math factorisation guide for families and teachers outside Singapore. What Secondary 2 students learn about factorising expressions, how Singapore teaches it, and how to practise it at home.
Factorisation is expansion in reverse.
It turns a sum back into a product, and that makes equations, fractions and graphs easier to handle.
In Singapore Mathematics, factorisation begins with common factors in Secondary 1. In Secondary 2, G3 students factorise expressions of the form ax + bx + kay + kby by grouping, factorise quadratic expressions ax² + bx + c, and use the algebraic identities.
Factorisation is then used to solve quadratic equations and simplify algebraic fractions. It returns in Additional Mathematics with the factor theorem.
This guide is useful for families and teachers who want to:
- understand what Singapore expects in Secondary 2 factorisation;
- teach the different forms in a clear order;
- prepare a student who is moving into a Singapore secondary school; or
- support a student using Singapore Math materials in another country.
Quick facts
Level: Secondary 2 (G3 Mathematics), building on common factors from Secondary 1
Strand: Number and Algebra (N5 Algebraic expressions and formulae)
Official source: MOE Secondary Mathematics Syllabuses (2020 Secondary 1 cohort onwards) and SEAB G3 Mathematics syllabus K310 for the SEC from 2027 (O-Level 4052 in 2026)
Comes after: Expansion and Algebraic Identities and Prime Factorisation, HCF and LCM
Leads to: Quadratic Equations and Algebraic Fractions
What Factorisation Means in Singapore Mathematics
To factorise an expression is to write it as a product of factors.
6x + 15 = 3(2x + 5). x² + 7x + 12 = (x + 3)(x + 4).
The idea matches factorising numbers, where 12 = 3 × 4. In algebra, the factors are expressions.
A complete factorisation leaves nothing that can be factorised further. 4x + 8 = 2(2x + 4) is not finished. 4(x + 2) is.
Every factorisation can be checked by expanding. If the expansion does not return the original expression, the factorisation is wrong.
Where Factorisation Sits in the Singapore Syllabus
In MOE’s teaching syllabus for G3 Mathematics, factorisation is spread across two years.
- Secondary 1: use brackets and extract common factors.
- Secondary 2: factorisation of linear expressions of the form ax + bx + kay + kby.
- Secondary 2: factorisation of quadratic expressions ax² + bx + c.
- Secondary 2: use of the identities (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and a² − b² = (a + b)(a − b).
Read from right to left, the identities also factorise expressions such as x² − 9 and x² + 6x + 9.
Factorising quadratics is then used to solve quadratic equations, also in Secondary 2.
G2 Mathematics also includes factorisation of these forms. MOE’s G2 sequence places some algebra items later than G3 does.
| Form | Example | Method |
|---|---|---|
| Common factor | 6x² + 9x = 3x(2x + 3) | Take out the highest common factor |
| Grouping | ax + bx + 2ay + 2by = (a + b)(x + 2y) | Group in pairs, then take out the common bracket |
| Quadratic | x² + 7x + 12 = (x + 3)(x + 4) | Find two numbers with the right product and sum |
| Difference of two squares | x² − 25 = (x + 5)(x − 5) | Use a² − b² = (a + b)(a − b) |
| Perfect square | x² − 10x + 25 = (x − 5)² | Use (a − b)² = a² − 2ab + b² |
How Singapore Teaches Factorisation
1. Start with the highest common factor
Students first look for a factor common to every term, both numbers and letters. This links to Prime Factorisation, HCF and LCM.
2. Factorise by grouping
With four terms, students group them in pairs so that each pair shares a factor and the same bracket appears twice.
3. Factorise quadratics with a leading coefficient of 1
For x² + bx + c, find two numbers that multiply to c and add to b.
4. Extend to ax² + bx + c
When a is not 1, students try factor pairs of a and of c, often set out in a cross or a multiplication frame. Splitting the middle term is another route. Each trial is checked by expanding.
5. Recognise the identities
x² − 49 is a difference of two squares. x² + 6x + 9 is a perfect square.
6. Always check by expanding
Expanding the answer must give back the original expression.
The order of these steps is the order of the questions a student should ask: is there a common factor, how many terms are there, and does an identity fit?
Worked Examples
Factorising a quadratic expression
Question: Factorise 2x² + 7x − 15 completely.
Step 1. Check for a common factor. There is none.
Step 2. Multiply a and c: 2 × (−15) = −30. Find two numbers that multiply to −30 and add to 7. They are 10 and −3.
Step 3. Split the middle term: 2x² + 10x − 3x − 15.
Step 4. Group in pairs: 2x(x + 5) − 3(x + 5).
Step 5. Take out the common bracket: (x + 5)(2x − 3).
Check: (x + 5)(2x − 3) = 2x² − 3x + 10x − 15 = 2x² + 7x − 15.
Common factor first, then an identity
Question: Factorise 3x² − 48 completely.
Step 1. Take out the common factor 3: 3(x² − 16).
Step 2. Recognise x² − 16 as a difference of two squares, with a = x and b = 4.
Step 3. 3x² − 48 = 3(x + 4)(x − 4).
Check: 3(x + 4)(x − 4) = 3(x² − 16) = 3x² − 48.
The word “completely” matters. Stopping at 3(x² − 16) is not complete, because x² − 16 still factorises.
Common Mistakes
- Forgetting the common factor. 2x² + 10x + 12 is attacked directly. Fix: take out 2 first, then factorise x² + 5x + 6 to get 2(x + 2)(x + 3).
- Getting the signs wrong. x² − x − 12 is written as (x − 4)(x − 3). Fix: the constant −12 is negative, so the two numbers have opposite signs. They are −4 and 3, giving (x − 4)(x + 3).
- Treating a sum of squares as a difference. x² + 9 is written as (x + 3)(x − 3). Fix: expand to test. (x + 3)(x − 3) = x² − 9, so x² + 9 does not factorise this way.
- Stopping too early. 4x² − 36 is left as 4(x² − 9) or (2x + 6)(2x − 6). Fix: factorise completely to get 4(x + 3)(x − 3).
- A sign slip when grouping. ax − ay − bx + by is grouped as a(x − y) − b(x + y). Fix: −bx + by = −b(x − y), so the answer is (x − y)(a − b).
- Not checking. A factorisation that looks right may not expand correctly. Fix: expand every answer before moving on.
Teaching Factorisation Outside Singapore
A few points are worth knowing when you use Singapore materials elsewhere.
- Spelling and terms. Singapore writes “factorise” and “factorisation”. US materials say “factor” and “factoring”, and use “greatest common factor” where Singapore says “highest common factor”.
- Timing. In Singapore, factorising quadratics is Secondary 2 in G3 Mathematics. Decide by readiness rather than age. The Singapore Math Grade Levels guide explains why direct conversions are unreliable.
- Prerequisites. Fast recall of multiplication facts helps students spot factor pairs. Negative numbers and expansion matter too. A student who cannot expand confidently is not ready to factorise.
- Methods. The syllabus names the content, not a method. Use the method the student applies reliably, and check by expanding.
- Calculators. An approved calculator may be used in both G3 Mathematics papers, but factorisation is done by hand and needs clear working.
How to Practise Factorisation at Home
A short, regular routine works better than one long weekend session.
- Warm up with factor pairs: list the pairs for 24 and 36, then the integer pairs that multiply to −18.
- Take out the highest common factor from three expressions.
- Factorise three quadratics with a leading coefficient of 1, including negative constants.
- Factorise one quadratic with a leading coefficient other than 1.
- Spot the identity in one expression, such as x² − 81 or x² + 14x + 49.
- Expand every answer to check, and keep a short list of errors to revisit.
Ten to fifteen minutes is enough when the work is focused.
Try These
- Factorise 8xy − 12y.
- Factorise x² − 2x − 15.
- Factorise 3x² + 10x + 8.
- Factorise ax + bx + 3ay + 3by.
Answers
- 4y(2x − 3). The highest common factor is 4y.
- (x − 5)(x + 3). −5 × 3 = −15 and −5 + 3 = −2.
- (3x + 4)(x + 2). Expanding gives 3x² + 6x + 4x + 8 = 3x² + 10x + 8.
- (a + b)(x + 3y). Group as x(a + b) + 3y(a + b).
What Comes Next
- In Secondary 2, factorisation is the first method for solving Quadratic Equations.
- In Algebraic Fractions, factorising the numerator and denominator lets students cancel common factors.
- Additional Mathematics extends factorisation to polynomials with the factor theorem, covered in Polynomials, Remainder and Factor Theorems.
A student who factorises calmly and checks by expanding is well prepared for each of these.
Frequently Asked Questions
When do Singapore students learn factorisation?
Taking out common factors is Secondary 1. Factorising by grouping and factorising quadratic expressions ax² + bx + c are Secondary 2 content in G3 Mathematics.
What does “factorise completely” mean?
It means nothing can be factorised further. Take out the highest common factor first, then check whether any bracket still factorises.
Is one method for quadratics required?
No. The syllabus names the content, not a method. Cross methods, multiplication frames and splitting the middle term all work when the checking is careful.
Does every quadratic expression factorise?
No. x² + 3x + 1, for example, cannot be factorised with integer coefficients. Equations such as x² + 3x + 1 = 0 are solved with the formula or by completing the square, in Secondary 3 or 4.
How is factorisation related to prime factorisation?
Prime factorisation writes a number as a product of primes, such as 60 = 2² × 3 × 5. Algebraic factorisation writes an expression as a product of simpler expressions. The thinking is the same.
Does G2 Mathematics include factorisation?
Yes. G2 includes these forms, although MOE’s G2 sequence places some algebra items later than G3 does.
Helpful Reading
- Singapore Mathematics | International Edition: Expansion and Algebraic Identities
- Singapore Mathematics | International Edition: Quadratic Equations
- Singapore Mathematics | International Edition: Algebraic Fractions
- Secondary Mathematics: Algebraic Identities, Expansion and Factorisation
- Secondary Mathematics: Quadratic Equations, Factorisation and Roots
- Why Algebra Becomes the Language of Secondary Mathematics
- MOE Secondary Mathematics Syllabuses (2020)
- SEAB G3 Mathematics Syllabus K310
Factorisation in Singapore Mathematics
Common factor first.
Then count the terms and look for a pattern.
Signs decide the pair.
Factorise completely.
Expand to check.
Taught this way, factorisation stops being guesswork.
It becomes a short set of questions asked in order, and that order carries a student into quadratic equations and beyond.
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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