Question

Using complete sentences, explain how the outcome of the Rational Root Theorem and Descartes’ Rule of Signs differ from one another

Answer 1

You probably need to try and just read about these two things and understand them for yourself first.
Rational roots theorem gives you a list of all the possible rational roots.
Descartes' rule of signs gives you a maximum number of positive real roots.

Answer 2

Rational root theorem is probably the simpler one to understand:
http://www.mathwords.com/r/rational_root_theorem.htm
Descartes' rule of sings isn't so bad either:
http://www.math.hmc.edu/funfacts/ffiles/20001.1.shtml