Factoring Polynomials and Finding Coefficients

Consider the polynomial expression given by:

$$P(x) = x^4 - 4x^3 + 6x^2 - 4x + 1$$

This polynomial can be factored into the form: $$P(x) = (x^2 + ax + b)(x^2 + cx + d)$$. If the polynomial is factored in this way, what is the value of $$a + b + c + d$$?