PROOF OF THE “SLIDE AND DIVIDE” METHOD OF FACTORING

Abstract

The "slide and divide" method of factoring quadratics $a x^2+b x+c$, where $a \neq 1$ is gaining popularity in algebra courses. It has many video demonstrations online and the individuals creating these videos enjoy the method. They emphasize the simplicity of its arithmetic and its ability to remove guess work from the factoring process.

The purpose of this paper is not to demonstrate this technique, but to prove it rigorously. There are websites that challenge the mathematical authenticity of the technique, claiming it to be a "shuffling of cards" [2] and not mathematically sound. Although the comments in [2] are not very kind toward the method, it still begs the question as to why it works. I set out to rigorously prove this technique. To see if it is mathematically and pedagogically valid and sound.

Received: September 1, 2025
Accepted: September 26, 2025