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O-LevelAdditional MathematicsFactors of polynomials4037/21 · May/June 2011 · Q56 Marks

The expression x³ + 8x² + px – 25 leaves a remainder of R when divided by x – 1 and a remainder of –R when divided by x + 2.

  1. (i)Find the value of p.[4]
  2. (ii)Hence find the remainder when the expression is divided by x + 3.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

  1. [1] (i) f(1) = 1 + 8 + p – 25 (= p – 16)
  2. [1] (i) f(-2) = -8 + 32 – 2p – 25 (= -2p – 1)
  3. [1] (i) p – 16 = -(-2p – 1) oe
  4. [1] (i) p = -17
  5. [1] (ii) Evaluates f(-3) or divides by (x + 3) to remainder
  6. [1] (ii) 71 (= 20 - 3p)

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2011 Paper 2 Variant 1, question 5.

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