A-LevelMathematicsAlgebra9709/33 · Oct/Nov 2019 · Q25 Marks

The polynomial 6x³ + ax² + bx − 2, where a and b are constants, is denoted by p(x). It is given that (2x + 1) is a factor of p(x) and that when p(x) is divided by (x + 2) the remainder is -24. Find the values of a and b.

The polynomial 6x³ + ax² + bx − 2, where a and b are constants, is denoted by p(x). It is given that (2x + 1) is a factor of p(x) and that when p(x) is divided by (x + 2) the remainder is -24. Find the values of a and b.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] Substitute x = -1/2 , equate result to zero and obtain a correct equation, e.g. 6/8 - a/4 - b/2 - 2 = 0
[*M1] Substitute x = – 2 and equate result to – 24
[A1] Obtain a correct equation, e.g. –48+4a-2b-2 = -24
[DM1] Solve for a or for b
[A1] Obtain a = 5 and b = -3

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Topic: Algebra, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 3 Variant 3, question 2.

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