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A-LevelMathematicsAlgebra9709/22 · Feb/Mar 2019 · Q46 Marks

Find the quotient when 4x³ + 8x² + 11x + 9 is divided by (2x + 1), and show that the remainder is 5.

  1. (i)Find the quotient when 4x³ + 8x² + 11x + 9 is divided by (2x + 1), and show that the remainder is 5.[3]
  2. (ii)Show that the equation 4x³ + 8x² + 11x + 4 = 0 has exactly one real root.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

  1. [M1] Carry out division at least as far as 2x² + kx
  2. [A1] Obtain quotient 2x² + 3x + 4
  3. [A1] Confirm remainder is 5
  4. [B1] State or imply equation is (2x+1)(2x² + 3x + 4) = 0
  5. [M1] Calculate discriminant of 3-term quadratic expression or equivalent
  6. [A1] Obtain −23 or equiv and conclude appropriately

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2019 Paper 2 Variant 2, question 4.

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