how does this factor...?

Identity · 2008-10-01 11:27:03

In a problem I need to find the maximum possible difference between any two variables in

The solutions give

What I don't get is how that factorises! This is a non-calculator problem and it confuses me how someone could first of all 1. See how to split up the polynomial so that just the right kind of stuff is in each place, 2. Know that the left bit actually factorises at all, 3. Factorise it.

Is there a method to the madness [other than simply inspection] or is this something you just need g0dlike intuition for?

TheDude · 2008-10-02 00:43:29

Perhaps one of the smarter people here will contradict me, but my guess is you just need to recognize by looking at it. Something I've noticed when helping my friends with math problems is that I'm just able to "see" things, like factorizations or substitutions, that they don't. Something like this problem just takes more practice (I certainly wouldn't have tried a factorization like that). I would say it's just a matter of practice and learning to recognize when you can use tricks like the ones they used for this problem.

Edit: That being said, in this particular problem you can see that the main factorization is similar to the original expression. I doubt you would be expected to be able to look at that problem and immediately see the correct factorization, but it would be reasonable for you to try things like (x + y + z)^2, (x - y - z)^2, etc. and finally work your way to the correct solution.

Last edited by TheDude (2008-10-02 00:47:04)

JaneFairfax · 2008-10-02 04:16:48

Perhaps these steps are clearer.

Its just completing the square by treating the LHS as a quadratic in x. Is this more intuitive than looking for factorizations?

Identity · 2008-10-03 11:34:39

Yeah it is! That's a good technique Jane, I'll have to remember it

Math Is Fun Forum

#1 2008-10-01 11:27:03

how does this factor...?

#2 2008-10-02 00:43:29

Re: how does this factor...?

#3 2008-10-02 04:16:48

Re: how does this factor...?

#4 2008-10-03 11:34:39

Re: how does this factor...?

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