O-LevelAdditional MathematicsFactors of polynomials4037/21 · Oct/Nov 2010 · Q25 Marks
The expression x³ + ax² – 15x + b has a factor x – 2 and leaves a remainder of 75 when divided by x + 3. Find the value of a and of b.
- (a)The expression x³ + ax² – 15x + b has a factor x – 2 and leaves a remainder of 75 when divided by x + 3. Find the value of a and of b.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [M1] Find f(2) or f(-3) or long division to remainder
- [A1] 8 + 4a – 30 + b = 0 or 4a + b = 22
- [A1] -27 + 9a + 45 + b = 75 or 9a + b = 57
- [M1] Solve simultaneous equations
- [A1] a = 7, b = -6
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