O-LevelAdditional MathematicsFactors of polynomials4037/22 · Oct/Nov 2011 · Q36 Marks
It is given that 2x – 1 is a factor of the expression 4x³ + ax² – 11x + b and that the remainder when the expression is divided by x + 2 is 25. Find the remainder when the expression is divided by x + 1.
- It is given that 2x – 1 is a factor of the expression 4x³ + ax² – 11x + b and that the remainder when the expression is divided by x + 2 is 25. Find the remainder when the expression is divided by x + 1.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [M1] f(1/2) = 0 or f(-2) = 25 (or f(-1) found)
- [A1] 1/2 + a/4 + b = 0 or a + b = 5 or a + 4b = 20
- [A1] -32 + 4a + 22 + b = 25 or 4a + b = 35
- [M1] Solve simultaneous equations
- [A1] a = 8, b = 3
- [A1√] f(-1) = 18
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