(50 points question!) How could you use Descartes' Rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial, as well as find the number of possible positive and negative real roots to a polynomial? Your response must include:

- A summary of Descartes' Rule and the Fundamental Theorem of Algebra. This must be in your own words.

- Two examples of the process

> Provide two polynomials and predict the number of complex roots for each.

> You must explain how you found the number of complex roots for each.

- At least 100 words in complete sentences with appropriate grammar and spelling.