Use rational root theorem and division to list the rational roots of the function below. \( g(x)=8 x^{3}-30 x^{2}-9 x+4 \) List the rational roots in order from least to greatest with commas and no spaces. Write fractions using a \( / \). No parentheses needed!

To find the rational roots of \( g(x)=8 x^{3}-30 x^{2}-9 x+4 \), we will use the Rational Root Theorem, which suggests that any potential rational root, in the form of \( p/q \), must have \( p \) as a factor of the constant term (4) and \( q \) as a factor of the leading coefficient (8). The possible rational roots are \( \pm 1, \pm 2, \pm 4, \pm 1/2, \pm 1/4, \pm 1/8 \). Testing these possibilities through synthetic division or direct substitution, we find \( x = 4/8 = 1/2 \), \( x = -1 \), and \( x = 2 \) are the roots. Thus, the rational roots in order are: -1, 1/2, 2