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O-LevelAdditional MathematicsFactors of polynomials4037/12 · Oct/Nov 2018 · Q98 Marks

The polynomial p(x) = ax³ + bx² + cx - 9 is divisible by x + 3. It is given that p'(0) = 36 and p''(0) = 86.

  1. (i)Find the value of each of the constants a, b and c.[6]
  2. (ii)Using your values of a, b and c, find the remainder when p(x) is divided by 2x-1.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] For substitution of x = -3 and equating to zero
  2. [M1] For differentiation in the form rx² + sx + t and substitution of x = 0
  3. [A1] nfww
  4. [M1] For further differentiation in the form vx + w of their p'(x) and substitution of x = 0
  5. [A1] nfww
  6. [A1] nfww
  7. [M1] For use of x = 1/2 in their p(x) from part (i)
  8. [A1]

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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, Oct/Nov 2018 Paper 1 Variant 2, question 9.

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