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O-LevelAdditional MathematicsFactors of polynomials4037/11 · May/June 2017 · Q25 Marks

It is given that p(x) = x³ + ax² + bx – 48. When p(x) is divided by x – 3 the remainder is 6. Given that p'(1) = 0, find the value of a and of b.

It is given that p(x) = x³ + ax² + bx – 48. When p(x) is divided by x – 3 the remainder is 6. Given that p'(1) = 0, find the value of a and of b.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[M1] attempt to find p(3)
[A1] 3a+b=9 oe
[M1] attempt to differentiate and find p'(1)
[A1] 2a+b=-3 oe
[A1] a =12, b = -27 for 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 2017 Paper 1 Variant 1, question 2.

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