A-LevelMathematicsAlgebra9709/22 · Oct/Nov 2025 · Q46 Marks
The polynomial p(x) is defined by 4 p(x) = x² - 10x³ +20x² - 30x+40.
- (a)Find the quotient when p(x) is divided by (x² + 3) and show that the remainder is –11. [3]
- (b)Hence find the real roots of the equation p(x) + 11 = 0. Give your answers in exact form. [3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [3] (a) Carry out division as far as x²±10x
- [3] (a) Obtain quotient x²−10x+17
- [3] (a) Confirm remainder is −11
- [3] (b) State or imply that equation is (x² + 3)(x² −10x+17) = 0
- [3] (b) Attempt solution of their three-term quadratic quotient from (a) to give two exact roots
- [3] (b) Obtain 5±√8 or 5±2√2 and no other solutions
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