Polynomials
Gujarat Board · Class 9 · Mathematics
Quick revision notes for Polynomials — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction to Polynomials
- A polynomial is an algebraic expression with variables having whole number exponents only
- Polynomials contain terms with variables, coefficients, and constants
- The general form is: p(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀
Classification of Polynomials
- Polynomials are classified by number of terms and degree
- By terms: Monomial (1 term), Binomial (2 terms), Trinomial (3 terms)
- By degree: Linear (degree 1), Quadratic (degree 2), Cubic (degree 3)
Zeros of Polynomials
- Zero of polynomial p(x) is value 'a' such that p(a) = 0
- Linear polynomials have exactly one zero
- Zero of polynomial corresponds to x-intercept of its graph
Remainder Theorem and Factor Theorem
- Remainder Theorem: When p(x) is divided by (x-a), remainder is p(a)
- Factor Theorem: (x-a) is factor of p(x) if and only if p(a) = 0
- These theorems connect polynomial division with evaluation
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Polynomials covers several key topics that are frequently asked in Gujarat Board Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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