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)

Check by expanding your answer



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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]

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Factoring

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

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