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O-LevelAdditional MathematicsFactors of polynomials4037/11 · May/June 2012 · Q25 Marks

The expression 2x³ + ax² + bx – 30 is divisible by x + 2 and leaves a remainder of –35 when divided by 2x – 1. Find the values of the constants a and b.

  1. The expression 2x³ + ax² + bx – 30 is divisible by x + 2 and leaves a remainder of –35 when divided by 2x – 1. Find the values of the constants a and b.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [M1] for substitution of x = -2 and equating to zero (2(-2)³ + a(-2)² + b(-2) - 30 = 0)
  2. [M1] for substitution of x = 0.5 and equating to -35 (2(0.5)³ + a(0.5)² + b(0.5) - 30 = -35)
  3. [M1] for solution of equations (4a - 2b = 46 and 0.25a + 0.5b = -5.25)
  4. [A1] a = 5
  5. [A1] b = -13

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About this question

Topic
Factors of polynomials, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 1 Variant 1, question 2.

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