Step 1 :The Rational Root Theorem states that the possible rational roots of a polynomial equation are given by the factors of the constant term divided by the factors of the leading coefficient.
Step 2 :In this case, the constant term is 27 and the leading coefficient is 3.
Step 3 :We need to find all the factors of 27 and 3.
Step 4 :The factors of 27 are \(1, 3, 9, 27\).
Step 5 :The factors of 3 are \(1, 3\).
Step 6 :We then divide each factor of 27 by each factor of 3 to get all possible rational roots.
Step 7 :The possible rational roots are \(\pm \frac{1}{3}, \pm 1, \pm 3, \pm 9, \pm 27\).
Step 8 :Final Answer: The possible rational zeros for the polynomial function are \(\boxed{\pm \frac{1}{3}, \pm 1, \pm 3, \pm 9, \pm 27}\).