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Chapter Summary

Polynomials

Maharashtra Board · Class 9 · Mathematics

Summary of Polynomials for Maharashtra Board Class 9 Mathematics. Key concepts, important points, and chapter overview.

45 questions28 flashcards5 concepts

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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

Frequently Asked Questions

What are the important topics in Polynomials for Maharashtra Board Class 9 Mathematics?
Key topics in Polynomials include Decision tree for identifying whether an algebraic expression is a polynomial based on the exponents of variables, Step-by-step process to find the degree of a polynomial in one variable, Process to calculate degree for polynomials with multiple variables. These are the concepts Maharashtra Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Polynomials — Maharashtra Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Polynomials

All 16 chapters — Maharashtra Board Class 9 Mathematics Chapter Summary

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