O-LevelAdditional MathematicsFactors of polynomials4037/12 · May/June 2022 · Q67 Marks
The polynomial p(x) = 6x³ + ax² + 6x + b, where a and b are integers, is divisible by 2x−1. When p(x) is divided by x−2, the remainder is 120.
- (a)Find the values of a and b.[4]
- (b)Hence write down the remainder when p(x) is divided by x.[1]
- (c)Find the value of p″(0).[2]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] For p(1/2) equated to zero
- [B1] For p(2) equated to 120
- [M1 Dep] on both previous B marks, for solving their equations to obtain a and b
- [A1] a=17, b=-8
- [B1] -8 (FT on their integer b)
- [M1] For attempt to differentiate their p(x), may be implied by correct FT answer
- [A1] p''(0) = 34 (FT on 2× their integer a)
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