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
a^{2} +2ab +b^{2} = ( 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
a^{2} -2ab +b^{2} = ( 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