Factorise the polynomial 6x^​3- x² - 46x - 15

Answer :

Factorise : 6x^​3- x² - 46x - 15 

$\Rightarrow$6x^​3-18 x² + 17 x² + 5x - 51 x - 15 

$\Rightarrow$6x^{3 ​}+ 17 x² + 5x -18 x² - 51 x - 15 

$\Rightarrow$ x ( 6x^{2 ​}+ 17 x + 5 ) -3 ( 6x^{2 ​}+ 17 x + 5 )

$\Rightarrow$ (  x - 3 ) ( 6x^{2 ​}+ 17 x + 5 )

$\Rightarrow$ (  x - 3 ) ( 6x^{2 ​}+ 15 x + 2 x + 5 )

$\Rightarrow$ (  x - 3 ) ( 6x^{2 ​}+ 2 x + 15 x + 5 )

$\Rightarrow$ (  x - 3 ) [ 2x ( 3x + 1 ) + 5 ( 3x + 1 ) ]

$\Rightarrow$ (  x - 3 )  ( 2x  + 5 ) ( 3x + 1 )                                      ( Ans )