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O-LevelAdditional MathematicsFactors of polynomials4037/22 · May/June 2018 · Q36 Marks

It is given that x + 3 is a factor of the polynomial p(x) = 2x³ + ax² – 24x + b. The remainder when p(x) is divided by x − 2 is -15. Find the remainder when p(x) is divided by x + 1.

Mark scheme

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

[M1] p(-3) = 0 or p(2) = -15 stated or implied
[A1] -54 + 9a + 72 + b = 0 or better
[A1] 16 + 4a - 48 + b = -15 or better
[M1] Solves a pair of simultaneous equations in a and b; condone one sign or arithmetic error in their solution; as far as finding one unknown
[A1] a = -7, b = 45
[A1] 60 cao

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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 2018 Paper 2 Variant 2, question 3.

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