Question 982312
Divide each of those choices by  2x-3, using polynomial division; and see which gives the specified quotient and remainder.


Here, testing just choice A:



_____________|
_____________|_________3x^2_______2x__________4__________(the quotient line)
_____________|_______________________________________________
_____________|
2x-3_________|________6x^3_______-5x^2_________+2x________(divisor on left, dividend on right)
______________________6x^2_______-9x^2
______________________________________
______________________0__________4x^2___________2x
_________________________________4x^2___________-6x
___________________________________________________
_________________________________0______________8x________0
________________________________________________8x________-12
______________________________________________________________
_________________________________________________0_________12


Remainder of 12;
Not choice A.



You try the others.