A-LevelMathematicsAlgebra9709/32 · Oct/Nov 2023 · Q35 Marks
3 The polynomial 2x³ + ax² – 11x + b is denoted by p(x). It is given that p(x) is divisible by (2x – 1) and that when p(x) is divided by (x + 1) the remainder is 12. Find the values of a and b.
- Find the values of a and b.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- M1 Substitute x = ½ and equate the result to zero Or divide as far as (2x-1)(x² + px+q) and equate constant remainder to zero.
- A1 Obtain a correct equation with powers evaluated e.g. 2(1/8)+a(1/4)-11(1/2)+b=0 or a+4b=21.
- M1 Substitute x=-1 and equate result to 12 Or divide as far as (x+1)(2x² + rx + s) and equate constant remainder to 12.
- A1 Obtain a correct equation with powers evaluated e.g. -2+a+11+b=12 or a+b=3.
- A1 Obtain a = -3, b=6
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