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

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