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A-LevelMathematicsAlgebra9709/22 · Feb/Mar 2018 · Q48 Marks

The polynomial p(x) is defined by p(x) = 4x³ + 4x² – 29x – 15.

  1. (i)Use the factor theorem to show that (x + 3) is a factor of p(x).[2]
  2. (ii)Factorise p(x) completely.[3]
  3. (iii)Hence, given that 2³u+2 + 4u+1 = 29 × 2u + 15, find the value of 2u and, using logarithms, find the value of u correct to 3 significant figures.[3]

Mark scheme

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

  1. [M1] Substitute x = -3 and simplify
  2. [A1] Obtain -108+36+87-15=0 or equivalent and conclude
  3. [M1] Attempt either division by x + 3 to reach at least partial quotient 4x² + kx or use of identity or inspection
  4. [A1] Obtain quotient 4x² - 8x - 5
  5. [A1] Conclude (x + 3)(2x - 5)(2x + 1)
  6. [B1] Identify 2u = 5/2 (Ignoring other values at this stage)
  7. [M1] Apply logarithms and use power law for 2u = c where c > 0
  8. [A1] Obtain u = 1.32 And no other values

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Feb/Mar 2018 Paper 2 Variant 2, question 4.

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