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4PM1/01 Jan 2020, Question 3: Solving Cubic Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 6 marks

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The question, in short

A cubic px³ − 31x² + 25x + 12 has factor (x − 4); show p = 6, then solve the cubic 6x³ − 31x² + 25x + 12 = 0 with clear algebraic working.

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Part (a) · 2 marks

Use the factor (x − 4) to show that the constant p equals 6.

  1. 1Factor theorem: substitute x = 4 and set equal to 0
  2. 264p − 31 × 16 + 25 × 4 + 12 = 0
  3. 364p − 496 + 100 + 12 = 0
  4. 464p = 384, so p = 6

Answerp = 6 shown

Part (b) · 4 marks

Solve 6x³ − 31x² + 25x + 12 = 0, showing clear algebraic working.

  1. 1Divide by (x − 4): 6x³ − 31x² + 25x + 12 = (x − 4)(6x² − 7x − 3)
  2. 26x² − 7x − 3 = (2x − 3)(3x + 1)
  3. 3(x − 4)(2x − 3)(3x + 1) = 0
  4. 4x = 4, x = 3/2, x = −1/3

Answerx = 4, x = 3/2, x = −1/3

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