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O-LevelAdditional MathematicsFactors of polynomials4037/21 · May/June 2020 · Q36 Marks

DO NOT USE A CALCULATOR IN THIS QUESTION. p(x) = 15x³ +22x² - 15x+2

  1. (a)Find the remainder when p(x) is divided by x+1.[2]
  2. (b)(i)Show that x+2 is a factor of p(x).[1]
  3. (b)(ii)Write p(x) as a product of linear factors.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] Finds p(-1)
  2. [A1] 24
  3. [B1] p(-2) = 15(-8) + 22(4) - 15(-2) + 2 = 0
  4. [M1] Attempt to find the quadratic factor
  5. [A1] 15x²-8x + 1
  6. [A1] (x+2)(3x-1)(5x-1) oe, cao
  7. If zero scored, SC1 for an answer of (x+2)(3x-1)(5x-1) without working.

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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 2020 Paper 2 Variant 1, question 3.

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