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Polynomials

Maharashtra Board · Class 9 · Mathematics

Quick revision notes for Polynomials — Maharashtra Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions28 flashcards5 concepts

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Key Topics to Revise

1

Introduction to Polynomials

  • An algebraic expression in which all the powers (exponents) of the variable(s) are whole numbers (0, 1, 2, 3, …) is called a polynomial.
  • Whole numbers include 0, 1, 2, 3, 4, … (non-negative integers).
  • Examples of polynomials: p³ − (1/2)p² + p, 6, x⁴ − 3x² + x + 5.
2

Degree of a Polynomial

  • For a polynomial in ONE variable: The highest power of the variable is called the degree of the polynomial.
  • Example: In 2x⁷ − 5x + 9, the degree is 7.
  • Example: In 10 (constant), degree = 0 because 10 = 10 × x⁰.
3

Standard Form, Index Form, and Coefficient Form

  • Standard Form: Write the polynomial with terms in DESCENDING order of powers of the variable. Example: x⁴ − 3x² + x + 5.
  • Index Form: Write the standard form and include ALL missing powers with coefficient 0. Example: x⁴ + 0x³ − 3x² + x + 5.
  • Coefficient Form: Write only the coefficients (numbers) in order from the highest power to the lowest. Example: (1, 0, −3, 1, 5).
4

Value of a Polynomial

  • When the variable in a polynomial is replaced by a specific number, the result is called the VALUE of the polynomial at that number.
  • If p(x) is a polynomial, then p(a) means the value of the polynomial when x = a.
  • To find p(a): substitute x = a in every term of the polynomial and simplify.

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Full Notes

Key Concepts

A polynomial is an algebraic expressionFor a polynomial in one variableStandard FormBased on the number of termsAddition/Subtraction

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.

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All 16 chapters — Maharashtra Board Class 9 Mathematics Revision Notes

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