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O-LevelAdditional MathematicsFactors of polynomials4037/12 · Oct/Nov 2021 · Q69 Marks

DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial `p(x) = 10x³ + ax² -10x+b`, where a and b are integers, is divisible by `2x+1`. When `p(x)` is divided by `x+1`, the remainder is -24.

  1. (a)Find the value of a and of b.[4]
  2. (b)Find an expression for p(x) as the product of three linear factors.[4]
  3. (c)Write down the remainder when p(x) is divided by x.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [M1] For use of the factor theorem
  2. [M1] For use of the remainder theorem
  3. [M1 Dep] on both previous M marks for solution of their equations without using a calculator
  4. [A1] a = -27, b = 3
  5. [M1] Allow for observation or algebraic long division. Their a and b must be integers.
  6. [A1] (2x+1)(5x²-16x+3)
  7. [M1] for attempt to factorise their 3-term quadratic
  8. [A1] all correct from fully correct working
  9. [B1] FT on their (integer) b

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2021 Paper 1 Variant 2, question 6.

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