Solved Examples on Factorization

In this section you can see Solved Examples on Factorization. Go through them carefully and then solve your question.

Solved Examples on Factorization

Using common factor

1) 4x + 8

Here , 4 is a common factor

4( x +2 ) are the factors .

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2) 8x^2 + 4x

Here , 4x is a common factor

= 4x( 2x +1) are the factors.

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3) 3x^3 + 6x^2 + 9

Here, 3 is a common factor

= 3( x
3 + 2x 2 3
are the factors.

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Using Identities

1) 4x
2 + 20 x +25

Here first and last term are perfect square so we will use an identity of
a2 +2ab +b2 = ( a+b)2

(2x )
2 + 2 (2x)(5) +(5) 2

=(2x + 5)
2

Factors are (2x +5)(2x +5)

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2) 9x
2 - 6x +1

Here first and last term are perfect square so we will use an identity of
a2 -2ab +b2 = ( a-b)2

(3x )
2 - 2 (3x)(5) +(1) 2

=(3x - 1)
2

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3) a
2 - b 2 - c 2 + d 2 - 2(ad - bc)

Solution :
a
2 - b 2 - c 2 + d 2 - 2(ad - bc)

= a
2 - b 2 - c 2 + d 2 - 2ad + 2bc)

= (a
2 + d 2 - 2ad) + ( -b 2 - c 2 + 2bc)

= (a
2 - 2ad + d 2 ) - ( b 2 - 2bc + c 2 )

= (a - d)
2 - (b - c) 2

= ( a - d + b - c)[a - d -(b - c)][ use a
2 - b 2 = (a + b)(a - b)]

= ( a - d + b - c)(a - d - b + c)

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4) a
4 - 81

Solution :
a
4 - 81

= (a
2 ) 2 - (9) 2

= (a
2 + 9)(a 2 - 9)

= (a
2 + 9)[a 2 -(3) 2 ] [ use a 2 - b 2 = (a + b)(a - b)]

= (a
2 + 9)(a + 3)(a - 3) [ use a 2 - b 2 = (a + b)(a - b)]

Factoring

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

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