The most efficient methods for factoring polynomials, particularly quadratics, include using the Quadratic Formula, completing the square, and traditional factoring techniques. The Quadratic Formula is often favored for its reliability in finding roots quickly, while completing the square can provide deeper insights into the polynomial's structure. Traditional factoring is effective when the polynomial can be easily broken down into simpler binomials. The choice of method may depend on the specific polynomial and the solver's familiarity with each technique. Ultimately, selecting the right method enhances efficiency in polynomial factoring.