Find the square root of `4x^(6) - 12x^(5) + 9x^(4) + 8x^(3) - 12x^(2) + 4`

Explanation

To find the square root of the polynomial \(4x^6 - 12x^5 + 9x^4 + 8x^3 - 12x^2 + 4\), we can use the method of polynomial long division or synthetic division. Here’s a step-by-step solution:

### Step 1: Identify the structure of the polynomial
The given polynomial is:
\[ 4x^6 - 12x^5 + 9x^4 + 8x^3 - 12x^2 + 4 \]
We need to find its square root, which we will assume to be of the form \( (ax^3 + bx^2 + cx + d)^2 \).
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