A-LevelMathematicsAlgebra9709/32 · Feb/Mar 2024 · Q13 Marks
Find the quotient and remainder when x⁴ - 3x³ + 9x² - 12x + 27 is divided by x² + 5.
- Find the quotient and remainder when x⁴ - 3x³ + 9x² - 12x + 27 is divided by x² + 5.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [M1] Commence division and reach partial quotient of the form x² +3x or x² -3x² + 9x² -12x + 27 = (x² + 5)(Ax² + Bx+C) + Dx + E or Ax⁴ + Bx³ + (5A + C)x² + 5Bx + 5C and reach A=1 and B = ±3
- [A1] Obtain quotient x² - 3x+4
- [A1] Obtain remainder 3x +7
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