Find all possible roots of the function \(f(x) = 3x^3 - 2x^2 - 5x + 2\)

Step 1 ：First, we find the potential rational roots using the Rational Root Theorem (RRT). According to the RRT, if a polynomial has a rational root \(\frac{p}{q}\), then \(p\) is a factor of the constant term (in this case, 2) and \(q\) is a factor of the leading coefficient (in this case, 3). Therefore, the potential rational roots are \(\pm1, \pm2, \pm\frac{1}{3}, \pm\frac{2}{3}\)

Step 2 ：Next, we substitute these potential roots into the polynomial function to see if they make the function equal to zero. Through this process, we find that \(-1, \frac{2}{3}\) are roots of the function.

Step 3 ：To find the remaining root, we can now use synthetic division or the factor theorem to divide the polynomial by \((x+1)(3x-2)\). We find that the remaining factor of the polynomial is \(3x - 2\), so the remaining root is \(x = \frac{2}{3}\).