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Factorisation can be defined as the product of multiple factors- usually simpler or smaller objects that are of the same kind. When an algebraic expression is factorised, it is written as a product of factors. These can be algebraic expressions, numbers or algebraic variables. In earlier chapters, you have studied the addition and subtraction of algebraic expressions and also how to multiply two expressions. In this chapter, you will study the division of one algebraic expression by another.
14.1 Introduction
14.1.1 Factors of Natural Numbers
14.1.2 Factors of Algebraic Expressions
14.2 What is Factorisation?
14.2.1 Method of common factors
14.2.2 Factorisation by regrouping terms
14.2.3 Factorisation using identities
14.2.4 Factors of the form (x+a) (x+b)
14.3 Division of Algebraic Expressions
14.3.1 Division of monomial by another monomial
14.3.2 Division of polynomial by a monomial
14.4 Division of Algebraic Expressions Continued
(Polynomial/Polynomial)
14.5 Summary
1. When an algebraic expression is factorised, it is written as a product of factors. These can be algebraic expressions, numbers or algebraic variables.
2. An irreducible factor is one such factor that cannot be expressed further as a product of factors.
3. A common factor method is a systematic way of factorising an expression.
4. When all the terms in a given expression do not have a common factor, the terms can be grouped in such a way that all the terms in each group have a common factor. When this is done, there emerges a common factor across all the groups leading to the required factorisation of the expression. This is the method of regrouping.
5. Factorisation by regrouping: Here, we should remember that any regrouping/rearrangement of the terms in the given expression may not lead to factorisation.
6. We know for the fact that in the case of numbers, the division is the inverse of multiplication. This idea is also appropriate/relevant to the division of algebraic expressions.
7. In the case of division of a polynomial by a monomial, we may carry out the division either by dividing each term of the polynomial by the monomial or by the common factor method.
8. In the case of division of a polynomial by a polynomial, we cannot proceed by dividing each term in the dividend polynomial by the divisor polynomial. Alternatively, we factorise both the polynomials and cancel their common factors.
9. In this chapter, we have considered only such divisions in which the remainder is zero.
For better understanding you can go through the following exercises for NCERT Solutions for Class 8 Chapter 14:
https://www.urbanpro.com/assets/new-ui/sharing_job.pngPublished on 2020-02-14 09:41:16 by arunima. Last Modified on 2020-02-14 09:41:16
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