GCSE Maths / Edexcel

Factorising into a single bracket

Find the highest common factor of terms and rewrite expressions using one bracket.

AlgebraFoundation and HigherGrades 3 to 5Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Factorising into a single bracket

Pearson Edexcel GCSE Maths algebra A4: simplify and manipulate algebraic expressions by factorising.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Factorising is the reverse of expanding brackets. Instead of removing brackets, you are putting brackets back in.

A factor is something that multiplies to make a term. For example, 6 is a factor of 6x and 12.

Look for the highest common factor shared by every term. The factor must divide into all terms, not just one of them.

Put the common factor outside the bracket. Then divide each original term by that factor to fill the bracket.

Check your factorisation by expanding it again. If it expands back to the original expression, it is correct.

If the question says factorise fully, take out the highest common factor, not just any common factor.

Key ruleab + ac = a(b + c)

Worked examples

Number factor

Factorise 6x + 12.

  1. Find the biggest number that divides both terms: 6 divides 6x and 12.
  2. Put 6 outside the bracket.
  3. Divide each term by 6: 6x / 6 = x and 12 / 6 = 2.

Answer: 6(x + 2)

Negative term

Factorise 8x - 20.

  1. The highest common factor is 4.
  2. 8x / 4 = 2x and -20 / 4 = -5.

Answer: 4(2x - 5)

Algebraic factor

Factorise 3x² + 9x.

  1. The common factor is 3x.
  2. 3x² / 3x = x and 9x / 3x = 3.

Answer: 3x(x + 3)

Common mistakes

  • Taking out a factor that is not shared by every term.
  • Not taking out the highest common factor when the question asks to factorise fully.
  • Losing the minus sign inside the bracket.
  • Forgetting that x is also a factor in expressions like 3x² + 9x.

Quick exercise

Try these before moving to the exam-style questions.

  1. Factorise 5x + 15.
  2. Factorise 6x - 18.
  3. Factorise 4x + 8.
  4. Factorise 10x - 25.
  5. Factorise 12x² + 6x.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Factorise 9x + 18.

factorisingcommon factorsingle bracket
Standard exam styleFoundation and HigherNon-calculator3 marks

Factorise fully 15x² - 10x.

factorise fullyalgebraic factornegative signs
ChallengeHigherEither4 marks

The area of a rectangle is 12x² + 18x. One side is 6x. Find an expression for the other side.

factorisingareaalgebraic divisionhigher reasoning