[ten_fingers]

The answer is simple, dirt simple: If you have to ask the question, then DON'T!

That is, we factor algebraic expressions if and only if (iff) we have a good reason to do so. If we don't have a good reason to factor, then there is no need to bother.

Yes, in high school, 'factoring' is seen as an important algebraic manipulation. It is. Then high school continues on and wants to factor whenever possible and for no reason other than it is possible. This is dumb.

Also, commonly there is more than one way to factor. Then high school gets all in a tizzy over which way is 'best'. Nonsense. Again, we factor for a reason we have in mind, and of several possible ways to factor we select the one for the reason we have in mind. Simple.

We factor when we have a reason to do so. Otherwise, f'get about it! High school teachers: Understand that now?

My authority: I hold a Ph.D. in the applied math of stochastic optimal control. I've taught math in college and graduate school. I've published peer-reviewed original research in applied math and mathematical statistics.

[majelix]

The obvious counterpoint here is that we're trying to teach skills before they're needed. After all, it would suck to have to rediscover Calculus on your own in the middle of your Physics II exam just because you didn't see a point to it at the time.

[ten_fingers]

Yes, and that's the way I learned in high school. At the time it appeared that we factored to achieve some 'artistic' goals of making the algebraic expressions 'look nice'. When later I concluded that we factored for some serious purposes and that the artistic goals of look nice were silly, I resented some of what I had been taught.

But the question on this thread is appropriate: "Why" do we factor? Sure, the reason in some of high school is just to learn how to factor so that we will be able to when we need to, say, working with integration by parts in calculus. But likely this tread and the students want a reason more substantial than just to learn for later. So, my answer was (say, beyond just learning) to factor when there was a good reason and otherwise just f'get about it, and basically that's the correct answer.

[batista]

>My authority: I hold a Ph.D. in the applied math of stochastic optimal control. I've taught math in college and graduate school. I've published peer-reviewed original research in applied math and mathematical statistics.

With all those one would expect better reasoning and/or better wording.

[ten_fingers]

No, my reasoning and wording are fine: Instead, "Things should be as simple as possible and not simpler"!