How to use Descartes Rule of signs to find positive & negative zeros

The video tutorial explains how to determine the variations in the sign of polynomial coefficients to find possible real zeros. It covers the process of calculating real zeros by subtracting even integers from the number of sign variations. The tutorial also discusses testing for negative real zeros using F(-X) and highlights the use of synthetic division and the rational zero test to identify zeros without a graphing calculator.

What conclusion can be drawn about the nature of zeros if there are no variations in sign when testing F of negative X?

How does synthetic division relate to identifying possible real zeros of a polynomial?