Identify the roots of -3x^3-21x^2+72x+540=0state the multiplicity of each root.

It took me awhile, but using the Rational Root Theorem and then synthetic division I got the first root.  If you don't know the RRT you'll be in heaps of trouble doing this type of problem.  I found the first root to be (x+6), then I did it again and got another root of (x+6) and the third one was (x-5).  So the roots of this polynomial (and there are 3 because this is a 3rd degree polynomial) are (x+6) with a multiplicity of 2, and (x-5).