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O-LevelAdditional MathematicsFactors of polynomials4037/21 · May/June 2023 · Q35 Marks

The diagram shows the graph of y = h(x) where h(x) = (x+a)²(b+cx) and a, b and c are integers. The curve meets the x-axis at the points (-2, 0) and (1.5, 0) and the y-axis at the point (0, 12).

  1. (a)Find the values of a, b and c.[2]
  2. (b)Use the graph to solve the inequality h(x) ≤ 9.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

  1. [2] a = 2, b = 3, c = -2
  2. [B1] for the critical values -3, -0.5, 1
  3. [B1] for −3 ≤ x ≤ −0.5
  4. [B1] for x ≥ 1

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2023 Paper 2 Variant 1, question 3.

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