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Grade 12 · Algebra
Polynomials: Remainder & Factor Theorem (Grade 12)
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/ 16
Answer all questions. Show all your working — marks are awarded for method as well as the final answer.
- 1Determine the remainder when f(x) = x³ − 4x² + x + 6 is divided by (x − 1).(2)
- 2Show that (x − 2) is a factor of f(x) = x³ − 4x² + x + 6.(2)
- 3Factorise f(x) = x³ − 4x² + x + 6 completely.(2)
- 4Solve for x: x³ − 4x² + x + 6 = 0(2)
- 5Determine the remainder when f(x) = 2x³ + x − 3 is divided by (x + 1).(2)
- 6If (x − 3) is a factor of f(x), what is f(3)?(2)
- 7Which values should you test first when factorising a cubic with constant term 12?(2)
- 8Solve for x: x³ − 7x + 6 = 0(2)
TOTAL: 16 marks