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O-LevelAdditional MathematicsFactors of polynomials4037/21 · May/June 2014 · Q45 Marks

The expression 2x³ + ax² + bx + 12 has a factor x - 4 and leaves a remainder of -12 when divided by x - 1. Find the value of each of the constants a and b.

  1. The expression 2x³ + ax² + bx + 12 has a factor x - 4 and leaves a remainder of -12 when divided by x - 1. Find the value of each of the constants a and b.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [M1] Attempt to find f(4) or f(1) or division to a remainder condone one error
  2. [A1] 128 + 16a + 4b + 12 = 0 or better (16a + 4b = -140)
  3. [A1] 2 + a + b + 12 = –12 or better (a + b = −26)
  4. [M1] Solves linear equations in a and b
  5. [A1] a = -3, b = -23 both

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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 2014 Paper 2 Variant 1, question 4.

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