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4MA1/1HR Jan 2023, Question 8: Simple Factorising

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

Factorise two algebraic expressions fully, then use the second factorisation to solve the related quadratic equation.

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

Part (a) · 2 marks

Factorise 18c³d² − 21c² completely.

  1. 1Identify common factors in 18c³d² and 21c²: both have 3 and c²
  2. 2Factor out 3c²: 3c²(6cd²) − 3c²(7)
  3. 3Write as single expression: 3c²(6cd² − 7)

Answer3c²(6cd² − 7)

Part (bi) · 2 marks

Factorise the quadratic y² − 3y − 18.

  1. 1Find two numbers that multiply to −18 and add to −3: +3 and −6
  2. 2Write factorised form: (y + 3)(y − 6)

Answer(y + 3)(y − 6)

Part (bii) · 1 mark

Using your factorisation, solve y² − 3y − 18 = 0.

  1. 1Use factorised equation: (y + 3)(y − 6) = 0
  2. 2Set each factor equal to zero: y + 3 = 0 or y − 6 = 0
  3. 3Solve: y = −3 or y = 6

Answery = −3 or y = 6

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