Is it Ok to only factor using the box method? Or should I learn the traditional way?

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X box factoring method:

The X box seems to be more versatile. I'm starting to get a little paranoid about this and I'm concerned if only learning this method will prevent me from understanding future textbooks.

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2 Answers

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To answer the question you asked in comments: the box method works in factoring because it is essentially the "inverse" of when you might have used the box method to multiply two binomials. There, you put the binomials on the outside of the box and multiplied to get the terms inside. Now, you're putting the terms on the inside and finding the GCF to determine the terms of the binomial.

I teach the box method when I'm teaching Algebra 1. However, like littleO suggests, it's something you can leave behind when you can visualize the binomials directly. It won't hurt your ability in Intermediate algebra or pre-calc at all, it'll just take a little extra pencil lead and the margins of your homework papers (which is what they're for). The strength of having the box method in your toolbox is that it can help to clarify things when it is time to factor quadratic expressions with leading coefficients like $6x^2+13x+6$. A lot of YouTube videos suggest doing those with guess-and-check, but with the AC method and the box method, you can do that without hassle. (That video goes on to use the grouping method instead of the box method. Stylistically, I think the grouping method gets awkward about 10% of the time and so I prefer to teach the box method.)

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The box method looks complicated.

I am not sure what level of education you have, but I am sure this method is not easy to follow and is quite error prone from a student.

Such methods may be introduced to make the student think, since the result itself is irrelevant. However, I guess this kind of approach may offset young students from learning mathematics because it requires more than the average skill (in my opinion).

Second degree equations could be solved by the Quadratic Formula. This requires knowledge of roots and requires care to apply it, but it does not require mental powers above the average. However, this is the classical approach to get results right.

Conclusion: If you have to learn the box method, then do. However, at some point of time you should get familiar with quadratic formula for future work in science.

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