Question

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

Answer 1

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 .

_________________________