Algebra 2

If 2x -3 is a factor in 6x^3 + 59x^2 - 25x - 150 then what are the remaining factors

             3x^2  +34x      +38.5

2x-3 |   6x^3 + 59x^2   - 25x - 150

            6x^3  - 9x^2

           --------------------------

                      68x^2     - 25x

                       68x^2 - 102x

                     --------------------------

                                    77x - 150

                                    77x - 115.5

                                    ---------------

                                          -34.5

You premise is wrong    2x-3 is NOT  a factor !!

Factor the following:
6 x^3+59 x^2-25 x-150

The possible rational roots of 6 x^3+59 x^2-25 x-150 are x = ±1/6, x = ±5/6, x = ±25/6, x = ±1/3, x = ±2/3, x = ±5/3, x = ±10/3, x = ±25/3, x = ±50/3, x = ±1/2, x = ±3/2, x = ±5/2, x = ±15/2, x = ±25/2, x = ±75/2, x = ±1, x = ±2, x = ±3, x = ±5, x = ±6, x = ±10, x = ±15, x = ±25, x = ±30, x = ±50, x = ±75, x = ±150. Of these, x = 5/3, x = -3/2 and x = -10 are roots. This gives 3 x-5, 2 x+3 and x+10 as all factors:
Answer: | 
| (3 x-5) (2 x+3) (x+10)