# NCERT Class 8 Mathematics Chapter 14 Factorisation CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Factorisation

### Factorisation of Algebraic Expression

• When we factorise an algebraic expression, we write is as a product of factors. These factors may by numbers, algebraic variables or algebraic expressions
• The expression it can be written as a product of factors.

The factors 2,3, x and are irreducible factors of .

### Method of Factorisation

 Name Working Common factor method We can look at each of the term in the algebraic expression, factorize each termThen find common factors to factorize the expressionExample Factorisation by regrouping terms First we see common factor across all the termsWe look at grouping the terms and check if we find binomial factor from both the groups.Take the common binomial factor outExample Factorisation using identities Use the below identities to factorise it Factorisation of the form Given We find factors a and b of q (i.e.. . , the constant term) such that and Now expression can be writtenOrOrOr which are the requiredFactors.ExampleNow and

### Division of Algebraic Expression

Division of algebraic expression is performed by factorisation of both the numerator and denominator and then cancelling the common factors.

Steps of division

• Identify the numerator and denominator
• Factorise both the numerator and denominator by the technique of factorisation using common factor, regrouping, identities and splitting
• Identify the common factor between numerator and denominator
• Cancel the common factors and finalize the result

Example

Here dividend

Divisor

Quotient

So, we have

In general, however, the relation is

When reminder is not zero

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