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O-LevelAdditional MathematicsFactors of polynomials4037/12 · May/June 2013 · Q78 Marks

It is given that f(x) = 6x³ – 5x² + ax + b has a factor of x + 2 and leaves a remainder of 27 when divided by x – 1.

  1. (i)Show that b = 40 and find the value of a.[4]
  2. (ii)Show that f(x) = (x + 2)(px² + qx + r), where p, q and r are integers to be found.[2]
  3. (iii)Hence solve f(x) = 0.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] M1 attempt at f (-2) = 0 allow unsimplified
  2. [1] M1 attempt at f (1) = 27 allow unsimplified
  3. [1] A1 for b = 40, B1 for a = -14
  4. [1] B1 for b = 40, B1 for a = -14
  5. [2] B2, 1, 0 -1 each error
  6. [1] B1 for dealing with quadratic factor either by use of formula, completing the square or use of b²-4ac to show that there are no real solutions
  7. [1] x = -2 B1

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2013 Paper 1 Variant 2, question 7.

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