Solved Examples on Factorization

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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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