A-LevelMathematicsAlgebra9709/21 · May/June 2019 · Q58 Marks
The polynomial p(x) is defined by p(x) = 5x³ + ax² + bx – 16, where a and b are constants. It is given that (x – 2) is a factor of p(x) and that the remainder is 27 when p(x) is divided by (x + 1).
- (i)Find the values of a and b.[5]
- (ii)Hence factorise p(x) completely.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Substitute x = 2 and equate to zero
- [M1] Substitute x = -1 and equate to 27
- [A1] Obtain 4a + 2b =-24 and a-b = 48 or equivalents
- [M1] Solve a relevant pair of simultaneous linear equations
- [A1] Obtain a = 12, b = -36
- [M1] Divide by x-2 at least as far as the x term to obtain 5x² + (their a+10)x...
- [A1] Obtain 5x² + 22x + 8
- [A1] Obtain (x-2)(5x + 2)(x + 4)
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