Solve `3x^(4) -8x^(3) -6x^(2) + 8x + 3 = 0`.

Explanation

To solve the equation \(3x^4 - 8x^3 - 6x^2 + 8x + 3 = 0\), we will use the Rational Root Theorem and synthetic division to find the roots. Here’s a step-by-step solution:

### Step 1: Identify possible rational roots
Using the Rational Root Theorem, we can identify possible rational roots of the polynomial. The possible rational roots are the factors of the constant term (3) divided by the factors of the leading coefficient (3).

Factors of 3: ±1, ±3
Factors of 3: ±1, ±3

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