Factorization by Common Factor

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.

Examples on Factorization by Common Factor method :

1) Factorize : 8x + 8

Solution :
The HCF of 8x and 8 is 8.

8x + 8 = 8 ( x + 1)

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2) Factorize: 4x2 - 6xy + 12x

Solution :
The HCF of 4x2 , 6xy and 12 x is 2x.

4x2- 6xy + 12x = 2x ( 2x -3y + 6)

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3) Factorize: 4x2 - 6xy + 12x

Solution :
The HCF of 4x2 , 6xy and 12 x is 2x.

4x2- 6xy + 12x = 2x ( 2x -3y + 6)
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3) Factorize : 35 a2 - 21 a2 b + 14 a2b2

Solution :
The HCF of 35 a 2, 21 a2 b and 14 a2b is 7 a2

a 2 - 21 a2 b + 14

a2b = 7 a2 ( 5 – 3b + 2 b2)
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Note : Taking HCF means divide each term with that HCF and put the quotient(answer) in the parenthesis.

Binomial as a common factor

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 ) – 5y ( a + b)

= ( a + b) ( 3x – 5y) [ ( a + b ) as a common factor ]
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2) 15 ( x – y)2 - 5x (x – y) - x + y

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

= ( x – y) [ 15( x – y) – 5x – 1 ]

= ( x – y ) ( 15x – 15y – 5x – 1)

= ( x – y) ( 10x – 15y – 1)
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3) 15x2(x + y) - 3 (x + y)

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

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

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

Factoring

Factorization by common factor
Factorization by Grouping
Factorization using Identities
Factorization of Cubic Polynomial
Solved Examples on Factorization