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( x3 + 2x23
are the factors.

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Using Identities

1) 4x2 + 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) 9x2 - 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) a2 - b2 - c2 + d2 - 2(ad - bc)

Solution :
a2 - b2 - c2 + d2 - 2(ad - bc)

= a2 - b2 - c2 + d2 - 2ad + 2bc)

= (a2 + d2 - 2ad) + ( -b2 - c2 + 2bc)

= (a2 - 2ad + d2) - ( b2 - 2bc + c2)

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

= ( a - d + b - c)[a - d -(b - c)][ use a2- b2 = (a + b)(a - b)]

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

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4) a4 - 81

Solution :
a4 - 81

= (a2)2 - (9)2

= (a2 + 9)(a2 - 9)

= (a2 + 9)[a2 -(3)2] [ use a2- b2 = (a + b)(a - b)]

= (a2 + 9)(a + 3)(a - 3) [ use a2- b2 = (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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