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12. Factorisation

The chapter covers the concepts of factorization including the identification of factors of natural numbers and algebraic expressions. It explains various methods for factorizing algebraic expressions through common factors, regrouping, and identities. The division of algebraic expressions is also introduced, presenting methods for dividing monomials and polynomials.

Sections

Factorisation

This section covers the concept of factorisation, emphasizing how numbers and algebraic expressions can be expressed as products of factors.

12 Section Overview

Start current section content and materials

12.1 Introduction

This section introduces the concepts of factorization in natural numbers and algebraic expressions, explaining factors, prime factors, and their applications.

12.1.1 Factors of natural numbers

This section introduces factors of natural numbers, illustrating their identification and importance in mathematics.

12.1.2 Factors of algebraic expressions

This section explores the concept of factors in algebraic expressions and different methods of factorisation.

12.2 What is Factorisation?

Factorisation is the process of writing an algebraic expression as a product of its factors, which may include numbers, variables, or other expressions.

12.2.1 Method of common factors

This section introduces the method of factorization using common factors by breaking down algebraic expressions into irreducible components.

12.2.2 Factorisation by regrouping terms

This section teaches the method of factorisation by regrouping terms in algebraic expressions, highlighting the process through specific examples.

12.2.3 Factorisation using identities

This section introduces factorisation through algebraic identities, demonstrating how to recognize and apply these identities to simplify expressions.

12.2.4 Factors of the form (x + a)(x + b)

This section discusses how to factor expressions in one variable, specifically those that can be expressed in the form of (xxxxx + aaaaa)(xxxxx + bbbbb), including strategies to find the correct factors.

12.3 Division of Algebraic Expressions

This section introduces the concept of dividing algebraic expressions, focusing on the division of monomials and polynomials.

12.3.1 Division of a monomial by another monomial

This section explains how to divide a monomial by another monomial using factorization.

12.3.2 Division of a polynomial by a monomial

This section explains how to perform division of a polynomial by a monomial, highlighting common factors and simplification methods.

12.4 Division of Algebraic Expressions Continued

This section discusses the division of polynomials by polynomials and focuses on factorization techniques for algebraic expressions.

Learning Objectives

  • When we factorise an expression, we write it as a product of factors including numbers and algebraic variables or expressions.

  • An irreducible factor cannot be expressed further as a product of factors.

  • A systematic approach, such as the common factor method, is essential for accurate factorization.

Key Concepts

Factorization

Writing an expression as a product of its factors, which may include numbers, algebraic variables, or expressions.

Common Factor Method

A systematic method of factorization involving identifying and separating common factors from terms.

Regrouping

Rearranging terms in an expression to facilitate factoring by identifying common factors within groups of terms.

Polynomial Division

The process of dividing a polynomial by another polynomial or monomial, which may involve cancellation of common factors.

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