O-LevelAdditional MathematicsFactors of polynomials4037/21 · May/June 2010 · Q36 Marks
It is given that x − 1 is a factor of f(x), where f(x) = x³ – 6x² + ax + b.
- (i)Express b in terms of a.[2]
- (ii)Show that the remainder when f(x) is divided by x−3 is twice the remainder when f(x) is divided by x−2.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [M1] (i) f(1) = 0
- [A1] (i) b = 5 - a only
- [M1] (ii) Finds f(2) and f(3)
- [M1] (ii) substitute b = 5-a or a = 5-b
- [A1] (ii) 2a – 22 or a – 11 (–2b – 12 or –b – 6)
- [A1] (ii) both correct
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