Used to factor polynomials when no other method works. The Rational Root theorem. If f(x) is a polynomial with INTEGER coefficients, then the candidates for every rational zero of f has the following form:
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Take each factor of p and divide it by each factor of q until all +/- fractional and integer factors can be found.
You will not just divide and get one answer, there will be multiple candidates for zerosThe rational zero theorem
Once you get one zero you can use synthetic division to factor and find the other zeros
Practice pg. 91 #7Rational root theorem Application
Ex: How many turning points does each graph have below?Turning Points on the graph