If x = -2 is a zero of the polynomial function f(x) = 2x^3 +9x^2-8x-36 which of the following is another zero if f(x)

We can use synthetic division to find all three zeros.  We have the first one, so finding the other 2 will be simple.  Doing the synthetic division gives us the depressed polynomial .  That can now be factored easily using the quadratic formula.  When we do that, we find that the other 2 zeros are x = 2 and x = -4.5.  It is literally impossible to demonstrate visually how to do synthetic division, but I'm guessing that if you are doing this you have probably learned it, along with long division, which would give you the same polynomial as does synthetic division.