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Polynomials

Gujarat Board · Class 9 · Mathematics

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

45 questions30 flashcards5 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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Key Topics to Revise

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.

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Full Notes

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)

Frequently Asked Questions

What are the important topics in Polynomials for Gujarat Board Class 9 Mathematics?
Key topics in Polynomials include Decision tree to identify whether an expression is a polynomial based on exponents and coefficients, Breaking down a polynomial into its constituent parts showing terms, coefficients, and degree, Mind map showing polynomial classification by number of terms. These are the concepts Gujarat Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Polynomials — Gujarat 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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