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.
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.
