O-LevelAdditional MathematicsFactors of polynomials4037/22 · Oct/Nov 2024 · Q35 Marks
DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is defined by p(x) = ax³ −3x² – 3x+b, where a and b are constants.
- (a)Given that x = 2 and x =-1 are roots of the equation p(x) = 0, find a and b.[3]
- (b)Solve the equation p(x) = 0.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- [B1] 8a - 12 - 6 + b = 0 oe
- [B1] -a - 3 + 3 + b = 0 oe
- [B1] a = 2, b = 2
- [B2] [2x³-3x²-3x+2 =] (x-2), (x+1), (2x-1) or (x²-x-2), (2x-1) and x = 2, 1/2, -1
- [B1] for (x-2) and (x+1) seen or (x²-x-2) seen
- [B1] for (x+1), (2x²-5x+2) or (x-2), (2x²+x-1) and correct factorisation or method of solution of the quadratic
- [B1] for 2x - 1 = (-3/2) or 2x - 1 = 3/2
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