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4024/12 Oct/Nov 2020, Question 3: Simple Factorising

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Factorise three algebraic expressions: 12t² − 4t, a(x − y) + b(y − x), and x² − 2x − 3.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Factorise 12t² − 4t by taking out the common factor.

  1. 1HCF of 12t² and 4t is 4t
  2. 212t² − 4t = 4t(3t − 1)

Answer4t(3t − 1)

Part (b) · 1 mark

Factorise a(x − y) + b(y − x), noting the sign change between the brackets.

  1. 1y − x = −(x − y)
  2. 2a(x − y) − b(x − y)
  3. 3= (a − b)(x − y)

Answer(a − b)(x − y)

Part (c) · 1 mark

Factorise the quadratic x² − 2x − 3 into two brackets.

  1. 1Two numbers with product −3 and sum −2: −3 and +1
  2. 2x² − 2x − 3 = (x − 3)(x + 1)

Answer(x − 3)(x + 1)

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Also searched as: 4024/12/O/N/20 · 4024_w20_qp_12 · 4024 w20 12 · question 3.
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