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2. Polynomials

Polynomials represent a significant class of algebraic expressions formed by combining variables, constants, and non-negative integer exponents. The chapter elaborates on various types of polynomials, their classifications based on degrees, the concepts of zeros and factors, and the application of algebraic identities in factorization. It emphasizes the importance of the Remainder and Factor Theorems in understanding polynomials in one variable as well as in multiple variables.

Sections

POLYNOMIALS

This section introduces polynomials, exploring their definitions, types, degree, and the concepts of zeroes and factorization.

2 Section Overview

Start current section content and materials

2.1 Introduction

This section introduces polynomials, their key characteristics, and significant theorems related to polynomial factorization.

2.2 Polynomials in One Variable

The section provides an overview of polynomials in one variable, introducing key definitions, types, and properties, including degrees and coefficients.

2.3 Zeroes of a Polynomial

This section introduces the concept of zeroes of a polynomial, explaining how to find them and their significance.

2.4 Factorisation of Polynomials

This section introduces the concept of factorisation of polynomials and the Factor Theorem, illustrating how to identify polynomial factors based on their roots.

2.5 Algebraic Identities

Algebraic identities are fundamental equations that hold true for any value of their variables.

2.6 Summary

This section outlines key concepts related to polynomials, including definitions, terms, and important theorems.

Learning Objectives

  • A polynomial in one variable is an algebraic expression of the form p(x) = anxn + an–1xn–1 + ... + a2x2 + a1x + a0.

  • Polynomials are classified into monomials, binomials, and trinomials based on the number of terms.

  • Each polynomial has a degree which indicates the highest power of the variable in the polynomial.

Key Concepts

Polynomial

An algebraic expression consisting of variables raised to non-negative integer powers, combined with coefficients.

Degree of a Polynomial

The highest exponent of the variable in the polynomial.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting