1. Let's state the problem: You want to find the possible zeros of a polynomial function. 2. The rule to find possible rational zeros is called the Rational Root Theorem. It says that any possible rational zero of a polynomial with integer coefficients is of the form $$\pm \frac{p}{q}$$ where: - $p$ is a factor of the constant term (the last number in the polynomial), - $q$ is a factor of the leading coefficient (the first number in the polynomial). 3. To apply this, first list all factors of the constant term. 4. Then list all factors of the leading coefficient. 5. Form all possible fractions $$\pm \frac{p}{q}$$ using these factors. 6. These fractions are the possible rational zeros you should test. 7. Remember, this method only finds possible rational zeros, not irrational or complex zeros. 8. Example: For the polynomial $$2x^3 - 3x^2 + 4x - 6$$ - Constant term is $$-6$$, factors: 1, 2, 3, 6 - Leading coefficient is $$2$$, factors: 1, 2 - Possible zeros: $$\pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{2}, \pm \frac{3}{2}$$ This is how you use the first and constant number to find possible zeros.