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

Method of Factorisation
NameWorking
Common factor method
  • We can look at each of the term in the algebraic expression, factorize each term
  • Then find common factors to factorize the expression
Example

Factorisation by regrouping terms
  • First we see common factor across all the terms
  • We look at grouping the terms and check if we find binomial factor from both the groups.
  • Take the common binomial factor out
Example

Factorisation using identitiesUse 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 written

Or

Or

Or

which are the required

Factors.

Example

Now 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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