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O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2012 · Q57 Marks

It is given that x – 2 is a factor of f(x) = x³ + kx² – 8x – 8.

  1. (i)Find the value of the integer k.[2]
  2. (ii)Using your value of k, find the non-integer roots of the equation f(x) = 0 in the form a ± √b, where a and b are integers.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [M1] (i) f(2)(= 8+4k-16-8) = 0
  2. [A1] (i) k = 4
  3. [M1] (ii) Find quadratic factor
  4. [A1] (ii) x² + 6x + 4
  5. [M1] (ii) Use quadratic formula or completing square
  6. [M1] (ii) -6±√(6²-4×(1)×4) / 2
  7. [A1√] (ii) -3±√5

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 2, question 5.

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