A-LevelMathematicsAlgebra9709/21 · Oct/Nov 2020 · Q25 Marks

The polynomial p(x) is defined by p(x) = x³ + ax² + bx + 16, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the remainder is 72 when p(x) is divided by (x – 2). Find the values of a and b.

The polynomial p(x) is defined by p(x) = x³ + ax² + bx + 16, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the remainder is 72 when p(x) is divided by (x – 2). Find the values of a and b.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[*M1] Substitute x=-2 and equate to zero
[*M1] Substitute x = 2 and equate to 72
[A1] Obtain 4a-2b+8=0 and 4a+2b-48=0 or equivalents
[DM1] Solve a pair of relevant linear simultaneous equations Dependent at least one M mark
[A1] Obtain a = 5, b=14

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Topic: Algebra, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 2 Variant 1, question 2.

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