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A systematic way of factorizing an expression is the Factorization by Common Factor. It consists of three steps:(i) Write each term of the expression as a product of irreducible factors.

(ii) Look for and separate the common factors.

(iii) Combine the remaining factors in each term in accordance with the distributive law.

1) Factorize : 8x + 8

The HCF of 8x and 8 is 8.

8x + 8 = 8 ( x + 1)

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2) Factorize: 4x

The HCF of 4x

4x

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3)

The HCF of 4x

4x

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3)

The HCF of 35 a

a

a

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In this method, find the binomial as a common factor and then divide the remaining term with that binomial and put that in parenthesis.

Examples

1) 3x

= ( a + b) ( 3x – 5y) [ ( a + b ) as a common factor ]

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2) 15 ( x – y)

= 15 ( x – y ) ( x – y) – 5x ( x – y) – ( x –y )

= ( x – y) [ 15( x – y) – 5x – 1 ]

= ( x – y ) (

= ( x – y) ( 10x – 15y – 1)

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3) 15x

H.C.F of two terms is 3x(x + y)

Taking 3x(x + y) is a common factor.

= 3x(x + y) [ 5x - 1]

• Factorization by common factor

• Factorization by Grouping

• Factorization using Identities

• Factorization of Cubic Polynomial

• Solved Examples on Factorization

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