What you said was that a quartic can always be factored into quadratics with possibly complex coefficients in disagreeing with the statement meaning that a quartic with real coefficients can always be factored into quadratics with real coefficients, a statement that is relevant for students in pre-algebra. So the fact that you can decompose a quartic into two quadratics, then decompose those into linear terms that may contain complex numbers, and then rearrange so that you get quadratics with complex coefficients does not contradict the fact that you can always decompose a quartic with real coefficients into two quadratics with real coefficients.
And why jump over real numbers like the square root of two to get into complex numbers? People in the thread had already talked about the rational root theorem and pointed that there was no rational root in this case.
And what do you mean by "irreducible cubic" unless you are restricting coefficients to real numbers.
Are you really saying that we should not expect a student in pre-algebra to factor x^2 - 2 = 0 but we should expect a solution to x^2 + 4 = 0.