Find all possible roots for the polynomial $3x^3-2x^2-5x+10$

Step 1 ：Step 1: Apply the Rational Root Theorem, which states that any rational root, $\frac{p}{q}$, of a polynomial equation $a{x}^n+b{x}^{n-1}+...+k=0$ can be expressed in the form $\frac{p}{q}$, where p is a factor of the constant term (k) and q is a factor of the leading coefficient (a).

Step 2 ：Step 2: For the polynomial $3x^3-2x^2-5x+10$, the constant term is 10 and the leading coefficient is 3. The factors of 10 are $\pm 1,\pm 2,\pm 5,\pm 10$ and the factors of 3 are $\pm 1,\pm 3$.

Step 3 ：Step 3: Form all possible fractions $\frac{p}{q}$ where p is a factor of 10 and q is a factor of 3. The possible rational roots are $\pm 1,\pm 2,\pm 5,\pm 10,\pm \frac{1}{3},\pm \frac{2}{3},\pm \frac{5}{3},\pm \frac{10}{3}$.

Step 4 ：Step 4: Substitute each possible root into the polynomial equation to see if it equals 0. After testing, we find that only $-2$ and $\frac{5}{3}$ are actual roots of the polynomial.