Question 769950
The factors of 4 are :  1, 2, 4
The factors of -6 are:  1, 2, 3, 6, -1, -2, -3, -6.


The values to check as roots for the function are plus-or-minus 1, 2, 4, 3/2, 3, 6, 1/2, 1/4.  Those are sixteen possible roots to check.  You will only be able to find THREE rational roots at most.  Test each possible root using synthetic division.  When a zero remainder occurs, then the tested root is a root of the function.