What topics are covered in the Polynomials chapter?

This chapter covers all essential concepts related to polynomials as per the CBSE Class 10 syllabus. You'll learn about polynomial definitions, types of polynomials (linear, quadratic, cubic), zeroes of polynomials, factor theorem, remainder theorem, and algebraic identities. The chapter also includes practical applications of polynomial concepts.

What learning resources are available for the Polynomials chapter?

The chapter provides comprehensive learning materials including video lessons explaining polynomial concepts, detailed notes with solved examples, NCERT textbook references, and additional practice problems. Visual aids and graphical representations are included to help you understand polynomial functions better.

Are there practice exercises and assessments for Polynomials?

Yes, the chapter includes a variety of practice exercises ranging from basic to advanced problems. You'll find chapter-wise quizzes, CBSE pattern-based tests, and application-based questions. Solutions with step-by-step explanations are provided for all practice problems to help you understand the concepts thoroughly.

How can I track my progress in understanding Polynomials?

The platform tracks your progress through each concept in the Polynomials chapter. You can monitor your performance in practice exercises, see which topics you've mastered, and identify areas needing more attention. The system provides personalized recommendations based on your quiz and test results.

Are there any special study tools for mastering Polynomials?

The chapter includes interactive tools like polynomial graphers to visualize functions, step-by-step polynomial solvers, and memory aids for important algebraic identities. These tools help you understand the graphical representation of polynomials and solve complex problems more effectively.

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2. POLYNOMIALS

Polynomials are essential mathematical expressions characterized by their degrees. This chapter explores the definitions, types, and geometric interpretations of polynomials, particularly focusing on their zeroes and the relationship between zeroes and coefficients. It also discusses the division algorithm for polynomials and highlights key concepts through various examples.

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2

Polynomials

This section covers the definition of polynomials, their types including linear, quadratic, and cubic polynomials, and the relationship between zeroes and coefficients.

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2.1

Introduction

This section provides a foundational understanding of polynomials, focusing on their degree and classifying them into linear, quadratic, and cubic categories.

Learning Practice
2.2

Geometrical Meaning Of The Zeroes Of A Polynomial

The section discusses the geometrical interpretation of the zeroes of polynomials, particularly for linear and quadratic forms.

Learning Practice
2.3

Relationship Between Zeroes And Coefficients Of A Polynomial

The section explains the relationship between the zeroes of a polynomial and its coefficients, particularly focusing on quadratic and cubic polynomials.

Learning Practice
2.4

Summary

This section summarizes key points regarding polynomials, particularly focusing on linear, quadratic, and cubic polynomials.

Learning Practice

References

NCERT Study Material

Class Notes

Memorization

What we have learnt

Polynomials of degrees 1, 2...
A quadratic polynomial in x...
The zeroes of a polynomial ...

Final Test

Revision Tests

Chapter FAQs

FAQs for CBSE Class 10 POLYNOMIALS Chapter

What we have learnt

Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
A quadratic polynomial in x with real coefficients is of the form ax2 + bx + c, where a, b, and c are real numbers with a ≠ 0.
The zeroes of a polynomial p(x) correspond to the x-coordinates of points where the graph of y = p(x) intersects the x-axis.
A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.
If α and β are the zeroes of a quadratic polynomial ax2 + bx + c, then the relationships are given by -b/a = α + β and c/a = αβ.
For cubic polynomials, there are established relationships among the coefficients and zeroes: -b/a = α + β + γ, c/a = αβ + βγ + γα, and -d/a = αβγ.

Key Concepts

Term: Polynomial

Definition: An expression consisting of variables raised to whole number powers, combined using addition, subtraction, multiplication, and coefficients.
Term: Linear Polynomial

Definition: A polynomial of degree 1 that has the general form ax + b.
Term: Quadratic Polynomial

Definition: A polynomial of degree 2 expressed in the form ax2 + bx + c where a ≠ 0.
Term: Cubic Polynomial

Definition: A polynomial of degree 3 expressed in the form ax3 + bx2 + cx + d where a ≠ 0.
Term: Zeroes of a Polynomial

Definition: The values of x that make the polynomial equal to zero, represented by the x-coordinates where the graph intersects the x-axis.

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