Final answer:
To find the number of rational zeros of a polynomial, use the Rational Zeros Theorem to list potential zeros as ratios of factors of the constant term and leading coefficient. Test these ratios to determine which are actual zeros of the polynomial.
Step-by-step explanation:
Understanding the Rational Zeros Theorem
To find the number of rational zeros using the Rational Zeros Theorem, you first identify the polynomial's leading coefficient and constant term. The possible rational zeros are the ratios of the factors of the constant term to the factors of the leading coefficient. Write out all possible ratios, reducing them to simplest form to eliminate duplicates. These represent the potential rational zeros of the polynomial.
For example, if you have a polynomial f(x) = 2x3 - 3x2 - 4x + 6, the leading coefficient is 2 and the constant term is 6. The factors of 6 are ± 1, ± 2, ± 3, and ± 6, and the factors of 2 are ± 1 and ± 2. You would form ratios from these sets, resulting in possible rational zeros of ± 1/1, ± 2/1, ± 3/1, ± 6/1, ± 1/2, and ± 3/2. After reducing, you have the possible rational zeros: ± 1, ± 2, ± 3, ± 6, ± 1/2, and ± 3/2.