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4MA1/1HR Jun 2025, Question 8: Factorising Quadratic Expressions

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

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The question, in short

Simplify two index expressions, then factorise a quadratic and use the result to solve the corresponding equation.

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

Part (a) · 1 mark

Simplify a⁶ × a¹⁰, giving the result as a single power of a.

  1. 1a⁶ × a¹⁰ = a⁶⁺¹⁰
  2. 2= a¹⁶

Answera¹⁶

Part (b) · 1 mark

Simplify c³⁰ ÷ c¹², giving the result as a single power of c.

  1. 1c³⁰ ÷ c¹² = c³⁰⁻¹²
  2. 2= c¹⁸

Answerc¹⁸

Part (ci) · 2 marks

Factorise the quadratic expression y² − 10y + 21 into two brackets.

  1. 1Need two numbers with product 21 and sum −10
  2. 2−3 and −7
  3. 3(y − 3)(y − 7)

Answer(y − 3)(y − 7)

Part (cii) · 1 mark

Using your factorisation, solve y² − 10y + 21 = 0 for y.

  1. 1(y − 3)(y − 7) = 0
  2. 2y − 3 = 0 or y − 7 = 0
  3. 3y = 3 or y = 7

Answer3, 7

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