Factorise: 2x^3+3x^2-5x-6

dhawanrajni010 dhawanrajni010

• 02.07.2020
• Math
• Primary School

answered • expert verified Factorise: 2x^3+3x^2-5x-6 See answers Saby123 Saby123

To Factorise -

2x³ + 3x² - 5x - 6

Solution -

According to the factor theorem , if for a polynomial , p ( x ) , p ( r ) is equal to 0 , ( x - r ) is a factor of P ( x ) .

Using this theorem -

If x = -1 ,

f ( x ) = 2x³ + 3x² - 5x - 6

f (- 1 ) = 2 ( -1 )³ + 3 ( -1 ) ² - 5 ( -1 ) - 6

=> f ( -1 ) = 0

=> ( x + 1 ) is a factor of 2x³ + 3x² - 5x - 6

Dividing 2x³ + 3x² - 5x - 6 by ( x - 1 )

=> 2x² + x - 6

Now ,

2x² + x - 6

=> 2x² + 4x - 3x - 6

=> 2x( x + 2 ) - 3 ( x + 2 )

=> ( 2x - 3 )( x + 2 )

Thus ,

p( x ) = 2x³ + 3x² - 5x - 6 can be Factorised as -

p ( x ) = ( 2x - 3 )( x + 2 )( x + 1 ) .

This is the required answer .

_________________________

harassis harassis

Answer:

required factor are (x+1) (2x-3) (x+2)

Step-by-step explanation:

Look at clip....!!!

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