Factorizing a Quadratic Expression with Reasoning

Abstract

It is not popularly realized that the factorization of a general quadratic expression basically requires solution to a hyperbola and a line. This fact is conspicuously pointed out and a few solutions to the problem are demonstrated that are scattered in the literature. In the high school level, the coefficients of a quadratic expression are mostly integers, and factorization is performed by the popular method of decomposition of the middle term. In this expository note, we have presented it in a simpler way that shows both insight and reasoning into the problem. Some other methods, namely, Linear Method, Average Method and Difference of two Squares Method are also discussed. Depending on the background, a reader may prefer a particular method to the others. The expository nature and artistry in presentation of the paper are expected to make the learning of the topic amusing and instructive.