AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 24

1 mark · Easy difficulty · Short Answer

Circle the expression which is a factor of 3x + 15 from the given choices: 3x, x + 12, x + 5, or x + 15.

Practise this question

Question

Question 24 asks to 'Circle the expression which is a factor of 3x + 15'. Four options are given horizontally: 3x, x + 12, x + 5, and x + 15. The question is worth 1 mark.

Mark scheme

Show the mark scheme Mark scheme for Question 24 shows a table with the correct answer 'x + 5' awarded a B1 mark with no additional comments.

How to answer it

Finding a Linear Factor of an Expression

What this question tests

This question assesses your ability to identify algebraic factors of a linear expression by factorising into a single bracket using the Highest Common Factor (HCF) of the terms.

Question 24

Multiple Choice • 1 Mark

Circle the expression which is a factor of   3x + 15

3x
x + 12
x + 5  ✔
x + 15

✅ Correct Answer

x + 5

Mark Scheme:
• B1: x + 5 circled or clearly indicated.

📐 Step-by-Step Method

  1. Find the HCF: Look at both terms in 3x + 15 . The highest common factor of 3 and 15 is 3.
  2. Divide each term by 3:
    • 3x ÷ 3 = x
    • 15 ÷ 3 = 5
  3. Write in factorised form:
    3x + 15 = 3(x + 5)
  4. Identify the factors: The factors of the expression are 3 and (x + 5). Therefore, x + 5 is the correct option.

💡 Key Knowledge

  • A factor is an expression that divides into another expression exactly without a remainder.
  • When factorising into a single bracket a(bx + c) , both a and (bx + c) are factors of the original expression.
  • To check your factorisation, expand the bracket:
    3 × x = 3x and 3 × 5 = 15 .

🧠 Exam Technique

  • Work it out before looking: Factorise the expression completely on the page before looking at the multiple-choice options to avoid being misled by plausible distractors.
  • Check by expanding: Multiply your chosen factor by the other factor ( 3 ) to see if you get back to 3x + 15 .
  • Make your answer unmistakable: Draw a clear ring around only one option. If you change your mind, cross out the incorrect one cleanly.

❌ Common Distractors & Traps

  • Choosing x + 12: Confusing division with subtraction (incorrectly doing 15 − 3 = 12 instead of 15 ÷ 3 = 5).
  • Choosing 3x: Mistaking a single term from the expression for a factor of the whole expression (15 cannot be divided by 3x to give a whole term).
  • Choosing x + 15: Dividing the first term by 3 to get x , but forgetting to divide the second term (15) by 3.

Topics

Algebra · 3.2.1 Notation, vocabulary and manipulation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.