Question 921286
The dividend coefficients are 2,-3,-5,0.  You must include all of them.  There is an alternative, but ...


A root of 3 means a binomial factor (divisor) of x-3.


The synthetic division without explanation goes this way:



_______3____|________2______-3______-5_______0
____________|
____________|_______________6_______9________12
____________|______________________________________
____________|_______2_______3________4_______12


The remainder is 12, which is NOT zero.
Three is not a root of the polynomial.