This is a project I have used in both Algebra II and PreCalculus classes to evaluate the Rational Root Theorem. I give them five problems to analyze and determine all the possible real roots using the Rational Root Theorem, Synthetic Division, and the Quadratic Formula. I have used this several time and been happy with the results.
While you (and the students) can verify their answers with a graphing calculator, what's important is the explanation of how they completed the work. The file gives detailed requirements and expectations for the final product.
I've also included an in-class version as well as an answer key for the overall roots.
See more unit lessons (specifically in Algebra II, AP Calculus, AP Statistics) at my store.
In-Depth No Prep Math Lessons