What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

F ( x ) = 6 x³ - 13 x² - 4 x + 15
f ( - 1 ) = 6 · ( - 1 ) - 13 · 1 - 4 · ( - 1 ) + 15 = - 6 - 13 + 4 + 15 = - 19 + 19 = 0
( 6 x³ - 13 x² - 4 x + 15 ) : ( x + 1 ) = 6 x² - 19 x + 15
 -6 x³  - 6 x²

         - 19 x²  -  4 x
         + 19 x² + 19 x
     
                      15 x + 15
                     -15 x - 15
                     
                      R ( x ) = 0
After that:
6 x² - 19 x + 15 = 6 x² - 10 x - 9 x + 15 =
= 2 x( 3 x - 5 ) - 3 ( 3 x - 5 ) = ( 3 x - 5 ) ( 2 x - 3 )

The completely factored form is: ( x + 1 ) · ( 3 x - 5 ) · ( 2 x - 3 )

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