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Syllabus

Polynomials — Syllabus

Gujarat Board · Class 9 · Mathematics

What Polynomials covers in Gujarat Board Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the Gujarat Board Class 9 Mathematics syllabus.

45 questions30 flashcards4 formulas & key relations5 concepts

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A labeled diagram illustrating the general form of a polynomial, distinguishing between real and complex polynomials by highlighting the nature of coefficients and variables. Also includes the definit
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4 Topics · Gujarat Board Class 9 Mathematics · 2026-27

Topics in Polynomials

1

Polynomials in One Variable – Definitions and Classification

  • A polynomial in one variable x is an expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₁x + a₀, where aₙ ≠ 0 and all exponents are whole numbers (0, 1, 2, 3, …).
  • Each part of the polynomial separated by + or – is called a TERM. For example, in 3x² – 5x + 2, the terms are 3x², –5x, and 2.
  • The number multiplied with the variable in each term is called its COEFFICIENT. In –5x, the coefficient is –5.
2

Zeroes of a Polynomial

  • The VALUE of a polynomial p(x) at x = a is found by substituting x = a in p(x) and calculating the result. It is written as p(a).
  • A real number 'a' is called a ZERO of polynomial p(x) if p(a) = 0.
  • Finding zeros means solving the equation p(x) = 0.
3

Remainder Theorem

  • The Remainder Theorem states: When a polynomial p(x) of degree ≥ 1 is divided by a linear polynomial (x – a), the remainder is p(a).
  • In other words, instead of performing long division, we can just substitute x = a in p(x) to find the remainder.
  • The divisor must be a LINEAR polynomial of the form (x – a). Note: if divisor is (x + a), then a is replaced by (–a), so substitute x = –a.
4

Factor Theorem and Factorisation of Polynomials

  • Factor Theorem: (x – a) is a factor of polynomial p(x) if and only if p(a) = 0.
  • Part 1: If p(a) = 0, then (x – a) is a factor of p(x).
  • Part 2: If (x – a) is a factor of p(x), then p(a) = 0.

Key Concepts

A polynomial in one variable xThe degree of a polynomialPolynomials are classified into types basedPolynomials are also classified byA zero of a polynomial p(x)

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Frequently Asked Questions

What are the important topics in Polynomials for Gujarat Board Class 9 Mathematics?
Key topics in Polynomials include Polynomials in One Variable – Definitions and Classification, Zeroes of a Polynomial, Remainder Theorem, Factor Theorem and Factorisation of Polynomials. 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 Gujarat Board Class 9 Mathematics Syllabus

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