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Revision Notes

Polynomials — Revision Notes

Maharashtra Board · Class 9 · Mathematics

Polynomials revision notes for Maharashtra Board Class 9 Mathematics: 4 topics in quick points. Part of the Maharashtra Board Class 9 Mathematics syllabus.

45 questions28 flashcards2 formulas & key relations5 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 Introduction to Polynomials, Degree of a Polynomial, Standard Form, Index Form, and Coefficient Form, Value of a Polynomial. Study these first, then practise questions on each for Class 9 exams.
How should I revise Polynomials for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Polynomials. Revise 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 Maharashtra Board Class 9 Mathematics Revision Notes

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