Polynomials and Factorisation
Kerala Board · Class 9 · Mathematics
Quick revision notes for Polynomials and Factorisation — Kerala Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
1. Introduction to Polynomials
- A polynomial is an algebraic expression with variables having non-negative integer powers only
- General form: p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀ where aₙ ≠ 0
- Examples: 3x² + 2x - 5, x³ - 4x + 1, 7 (constant polynomial)
2. Types of Polynomials
- Classification by degree: Linear (degree 1), Quadratic (degree 2), Cubic (degree 3)
- Classification by terms: Monomial (1 term), Binomial (2 terms), Trinomial (3 terms)
- Zero polynomial: all coefficients are zero, degree undefined
3. Value of Polynomial and Zeros
- Value of polynomial p(x) at x = a is p(a) - substitute a for x
- Zero of polynomial: value of x for which p(x) = 0
- Linear polynomial has exactly one zero
4. Remainder Theorem
- When polynomial p(x) is divided by (x - a), remainder = p(a)
- No need for actual division - just substitute x = a
- Works for any polynomial of degree ≥ 1
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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