[CAES] (x^4-4*x^3+2*x^2+4*x+4) Exact factorization of Quartic Polynomial

[Han]

I do not understand the desire to algebraically factor quartics into linear factors especially if the linear factors do not provide any direct insight to quartic itself. At least for quadratics, the linear factors \( (x-a)(x-b) \) one can quickly compute \( -( a+b) \) to get the linear coefficient and \( ab \) gives the constant term. Of course, this can be generalized, but it is not quite as simple for higher order polynomials. I would even put cubics into this category of "neat but not really useful" insofar as algebraic roots are concerned -- not useful for pedagogy nor everyday use.