How do you find the rational zeros of "p (x)"

Use the Rational Root Theorem.

Step-by-step explanation:

Any rational roots will be factors of the ratio of the constant (=p (0)) to the leading coefficient of the polynomial p (x). In the general case, that ratio is a rational number and the roots have numerator that is a factor of its numerator, and a denominator that is a factor of its denominator.

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To see how this works, consider the polynomial with rational roots b/a and d/c. Factors of it will be ...

p (x) = (ax - b) (cx - d) (other factors if p (x) is of higher degree)

The leading coefficient here is ac; the constant term is bd. The rational root theorem says any rational roots are factors of (bd) / (ac), which b/a and d/c are.