1. Decarte’s Rule and Rational Roots

2. Decarte’s Rule of Signs
Used to help see the number of possible zeros for positive, negative, and imaginary if you set it up in a chart.
First arrange in descending order according the powers.
The number of positive real zeros is the same as the number of sign changes of the coefficients, or less than it by an even number.
The number of negative real zeros is the same as the number of sign changes of the coefficients of the terms P(-x), or is less than it by an even number.
The number of imaginary zeros is whatever is left over in each case.
Example: 2x³ + 5x² - 2x -15

3. Rational Zero Test
Used to determine the possible rational zeros of a function.
We will first use two new letters p and q. P will always be equal to the constant term and q will always be equal to the first coefficient.
After identifying what p and q are equal to, we now need to find all the factors of p and all the factors of q(including the negatives). Once we have done that, we find all the possible combinations of p/q.
Example: Find all possible rational roots of 2x³ + 5x² - 2x -15