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)]

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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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