...or more formally known as "Completing the Factoring by Using the Multiplicative Property of 2." We're going to release it under Creative Commons, so feel free to use it in your classes too. Just make sure you give credit where credit is due.
Here it is. Bask in the glory!
Beautiful isn't it? So elegant. So simple. So WRONG!
I've been teaching this stuff for a while and haven't seen this misconception before. I thanked the student for providing us with the best wrong answer I've ever seen. He looked at me kinda funny then realized I was dead serious. I loved this.
What an opportunity to discuss why we do what we do. This student had the process for solving a quadratic equation by factoring cold. But he didn't understand why we set the equation equal to zero. I don't know about your students, but mine do pretty well with the What. It's the Why that drives this class. I was a bit surprised at how long it took for a student to step up and explain the error in a way that wasn't, "if you plug in the numbers they don't work."
I do my best to make my students think, but they still try to become good little algorithm followers.
The fight goes on.