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Chapter 12: Factorisation

    Introduction

    Factors of Algebraic Expressions

    Need of Factorisation

    Method of Common Factors

    Factorisation by grouping the terms

    Factorisation using Identities

    Factors of the form (x+a)(x+b) = x² + (a+b)x + ab

    Division of Algebraic Expressions

    Division of a Monomial by another Monomial

    Division of an Expression by a Monomial

    Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

    Exercise 12.1

    Exercise 12.2

    Exercise 12.3

    Exercise 12.4

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 12: Factorisation > Need of Factorisation

Need of Factorisation

We know that to factorise an algebraic expression, we write it as a product of factors. These factors may be numbers, algebraic variables or algebraic expressions.

Expressions like 3xy, 5x2y, 2x(y + 2), 5(y + 1)(x + 2) are already in factor form. They can't be simplified any further. We can also deduce their factors by simply looking at the expression at hand.

On the other hand, consider the expressions- 2x + 4, 3x + 3y, x2+5x, x2+5x+6. Here, it becomes less obvious what the factors for these expressions are. In order to solve this, there is a need for systematic methods to factorise expressions, i.e. to find their factors. Let's look at them.