The factorability of quadratics: motivation for more techniques

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations, this paper will demonstrate that the probability that a randomly selected quadratic with integer coefficients is factorable is extremely small. In addition to the ineffectiveness of factoring, this paper reveals some significant advantages associated with completing the square and the quadratic formula and that these techniques should be utilized more quickly, more often, and certainly before frustration mounts.