Finding the Value of p in Polynomial with a Double Root

Let $$ f(x) $$ be a polynomial function defined as:

$$ f(x) = 3x^4 - 8x^3 + px^2 + qx - 5 $$

Given that the function has a double root at $$ x = 2 $$, determine the value of $$ p $$ such that the polynomial can be expressed in the form $$ (x - 2)^2 (ax^2 + bx + c) $$, where $$ a, b, $$ and $$ c $$ are constants. What is the value of $$ p $$?