GCSE MATHS PRACTICE
GCSE Factorising Questions
Factorising reverses expanding: write an expression as a product by taking out a common factor. To factorise fully into a single bracket, use the highest common numerical factor and any variables shared by every term. Divide each term by that factor to find what belongs inside. This page covers algebraic common factors, not prime factorisation or quadratic factorisation into two brackets.
Updated 10 October 2026
Worked example
Factorise fully 18x + 30.
- The highest common factor of 18 and 30 is 6. The variable x is not shared by both terms.
- Divide each term by 6: 18x ÷ 6 = 3x and 30 ÷ 6 = 5. Place 6 outside the bracket: 6(3x + 5).
- Check by expanding: 6 × 3x + 6 × 5 = 18x + 30.
Answer: 6(3x + 5)
Practice questions
- 1
Factorise fully 8x + 12.
- 2
Factorise fully 15a − 25.
- 3
Factorise fully 12x² + 18x.
- 4
Factorise fully 14ab − 21a.
Show answers
- 1. 4(2x + 3)
- 2. 5(3a − 5)
- 3. 6x(2x + 3)
- 4. 7a(2b − 3)
Common mistakes
- Taking out only part of the common factor — Check both the numbers and the variables when asked to factorise fully.
- Losing the subtraction sign — Dividing a negative term by a positive factor leaves a negative term inside.
- Not checking the result — Expanding the brackets must recover the original expression.