IP AMaths Notes (Upper Sec, Year 3-4): 09) Polynomials
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Factor theorem, remainder theorem, and inequalities involving higher-degree polynomials for IP AMaths.
Last updated 30 Nov 2025
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- Start Here
- 1 Key results
- 2 Worked example - Factorisation
- 3 Worked example - Polynomial inequality
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 09) Polynomials cover?
A: Factor theorem, remainder theorem, and inequalities involving higher-degree polynomials for IP AMaths.
Polynomials underpin factorisation, curve sketching, and inequality solving. Memorise the theorems that convert substitution into proofs of factor status.
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These tools align with the SEAB GCE O-Level Additional Mathematics (4049) syllabus: factor and remainder theorems, Vieta relationships, and sign-chart reasoning for cubic inequalities.
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
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| Read time | What to take away |
| 1 second | Polynomial questions turn substitution into factor and remainder information. |
| 10 seconds | Use f(a) = 0 to prove x - a is a factor, then factor fully before solving inequalities or finding roots. |
| 100 seconds | Example: if f(2) = 0, divide by x - 2 first. The remaining quadratic often unlocks the full factorisation and the sign chart. |
1 Key results
- Factor theorem: if
