text: If the quartic is recognizable as being factorizable into lower degree polynomials then that is the best way to go. If it is not immediately recognizable, the next step is to use the Rational Roots Theorem to check for rational roots, and factor out the corresponding binomials by synthetic/long division if that is the case. \nIf there are no rational roots, then you're pretty much stuck with using the Ferrari's quartic formulas given on http://mathworld.wolfram.com/QuarticEquation.html (equations 36-39).