Solve `x^(3)-8x-3=0`.

Explanation

To solve the equation \( x^3 - 8x - 3 = 0 \), we will use the Rational Root Theorem and synthetic division.

### Step 1: Identify possible rational roots
According to the Rational Root Theorem, the possible rational roots of the polynomial can be the factors of the constant term divided by the factors of the leading coefficient. Here, the constant term is \(-3\) and the leading coefficient is \(1\).

The possible rational roots are:
\[
\pm 1, \pm 3
...