Polynomials — Chapter Summary
Maharashtra Board · Class 9 · Mathematics
Summary of Polynomials for Maharashtra Board Class 9 Mathematics. Key concepts: A polynomial is an algebraic, For a polynomial in one and Standard Form.
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Overview
A polynomial is an algebraic expression where all variables have non-negative integer (whole number) powers. Polynomials are fundamental building blocks in algebra and appear throughout mathematics. Unlike expressions like √y + 5 (where power is 1/2) or 1/y - 3 (where power is -1), polynomials only
Key Concepts
A polynomial is an algebraic expression
A polynomial is an algebraic expression where each term has variables raised to whole number (non-negative integer) powers. Examples: p(x) = x³ + 2x²
For a polynomial in one variable
For a polynomial in one variable, the degree is the highest power of that variable. For example, in 2x⁷ - 5x + 9, the degree is 7. For constant polyno
Standard Form
Standard Form: Polynomial written in descending powers of the variable, e.g., x⁴ - 3x² + x + 5. Index Form: All possible powers included with coeffici
Based on the number of terms
Based on the number of terms: Monomial (one term): 5x², -3m. Binomial (two terms): x² + 3, 2y - 7. Trinomial (three terms): x² + 5x + 6, m³ + 2m - 1.
Addition/Subtraction
Addition/Subtraction: Combine like terms by adding or subtracting their coefficients. Example: (5m³ - 7m³) = -2m³. Multiplication: Multiply each term
Learning Objectives
- Understand what constitutes a polynomial and identify polynomials from algebraic expressions
- Determine the degree of polynomials in one variable and multiple variables
- Convert polynomials between standard form, index form, and coefficient form
- Perform operations (addition, subtraction, multiplication, division) on polynomials
- Apply synthetic division when dividing polynomials by linear divisors
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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