1. Rational Root Theorem By: Yu, Juan, Emily

2. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.

3. How To Use It? First locate your q and p value. Example: 6x 4 - 2x 3 + 5x 2 + x -10 = 0 Your q would be 6 and your p value would be -10 because of 6 is your leading coefficient and -10 is your constant. (q = leading coefficient; first number of your polynomial, p = constant; last number of your coefficient) Next you list all the possible factors of both the coefficient and constant; your q and p. 6: ±(1, 2, 3, 6) -10: ±(1, 2, 5, 10 )

4. How To Use It? After listing out all of the factors of your leading coefficient and constant; your q and p. You would want to make a list of all of your possible zeros by dividing your p (leading coefficient) by your q (Constant). Using the example on the previous slide, your list of all of the possible zeros would be: p/q = ±(1, 2, 5, 10, ½, 5/2, 10/2, 1/3, 2/3, 5/3, 10/3, 1/6, 5/6, 10/6)

5. How To Use It? After that, with the list you came up with; p/q = ±(1, 2, 5, 10, ½, 5/2, 10/2, 1/3, 2/3, 5/3, 10/3, 1/6, 5/6, 10/6), those would be your possible zeros. Refer to the link below if you have further questions. http://www.youtube.com/watch?v=RXKfaQemt

6. How To Use It? Once you have your list of all of your possible zeros, using synthetic division; you can find your exact zeros for your polynomial. Refer to the link below for a review of Synthetic division: http://www.youtube.com/watch?v=bZoMz1Cy1T4

7. Practice Problem 4x 3 + 8x 2 + 16 Use the Rational Root Theorem for the polynomial above. Once you find the possible zeros for the polynomial equation above, use Synthetic division to find the exact zeros.