Finding the Leading Coefficient of a Polynomial Factor

Consider the polynomial function defined as:

$$f(x) = 2x^3 - 9x^2 + 12x - 4$$

To find the roots of this polynomial, we can apply the Rational Root Theorem and polynomial long division. First, determine potential rational roots based on the factors of the constant term and the leading coefficient. Then, perform polynomial division using one of the identified roots to factor the polynomial further.

Once you have fully factored the polynomial, find the value of the leading coefficient of the resultant quadratic factor.