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Subject: "Uses for factoring trinomials"     Previous Topic | Next Topic
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Matthew
guest
May-26-03, 09:33 PM (EST)
 
"Uses for factoring trinomials"
 
   I am a High School student now, and have started taking Algebra. I have learned several of the methods, and have seen how they could be used. However, I was at a loss to explain how factoring trinomials can be used. Not counting teaching/tutoring algebra, why would I need to know how to do this? I am not saying it is unnecessary, I would just like some facts.

Can you list a couple of occupations that require familiarity with it?

Is there an article somewhere detailing this topic, and also explaining how other semi-advanced concepts could be used?

Thanks for you help.

Matthew


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  Subject     Author     Message Date     ID  
Uses for factoring trinomials Matthew May-26-03 TOP
  RE: Uses for factoring trinomials RicBrad May-28-03 1
  RE: Uses for factoring trinomials alexb May-28-03 2
  RE: Uses for factoring trinomials Graham C May-30-03 3
  RE: Uses for factoring trinomials CSpeed Jun-02-03 4
     RE: Uses for factoring trinomials alexb Jun-03-03 5
         RE: Uses for factoring trinomials CSpeed0001 Jun-05-03 6
             RE: Uses for factoring trinomials Matthew Jun-12-03 7
     RE: Uses for factoring trinomials Matthew Jun-12-03 8
     RE: Uses for factoring trinomials Matthew Jun-12-03 9
  RE: Uses for factoring trinomials Matthew Jun-12-03 10

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RicBrad
Member since Nov-16-01
May-28-03, 11:22 PM (EST)
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1. "RE: Uses for factoring trinomials"
In response to message #0
 
   >I am a High School student now, and have started taking
>Algebra. I have learned several of the methods, and have
>seen how they could be used.

Maths is the best tool we have for understanding the world around us: an engineer can say, "this is how a turbine will react to a given force", and write down an set of equations, and then go on to design a power plant that will run a city. Anything manufactured has had a lot of maths applied in its design.

Unfortunately the maths used by engineers, scientists, economists and the rest requires a firm grounding in basic algebra. With high school maths you can work out all sorts of (slightly contrived) problems like how much carpet you need to buy or whatever, but the important applications of maths only come much later.

For now you will have to be satisfied with the beauty of maths - and even that only really comes out with the more complex bits introduced later.

>However, I was at a loss to
>explain how factoring trinomials can be used. Not counting
>teaching/tutoring algebra, why would I need to know how to
>do this? I am not saying it is unnecessary, I would just
>like some facts.

You can solve quadratic equations by factoring them, so problems that can be expressed this way could be solved by factorisation.

Sorry - I can't come up with a simple example - something like finding the box of maximum volume you can make out of a sheet of paper might work, but that needs differentiation as well. Anyone else got any examples?

>Can you list a couple of occupations that require
>familiarity with it?

Engineer, economist, scientist, mathematician, computer programmer, ... , anyone in a technical job.


A lot of people will tell you not to worry about the applications of maths, and I agree with that, but let me add that if you have the perseverance to carry on with maths you will find it has an amazing number of applications in almost every field.

Rich


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alexb
Charter Member
984 posts
May-28-03, 11:40 PM (EST)
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2. "RE: Uses for factoring trinomials"
In response to message #0
 
   >Can you list a couple of occupations that require
>familiarity with it?

Please do not get this personally, but I despise this kind of questions. I would be loath to look forward to an occupation that somehow required factoring trinomials in any essential way. Moreover, I am confident that, by the time you get a job, computers will do that fast and efficiently. There simply are not and won't be professions that require that operation as a prerequisite for a successful career.

This said, there are uncountable places where factoring trinomials is useful. Worse yet, with a little degree of creativity you may come up with new applicaions. This is most important: the less you know, the less creative you can be. You never know what knowledge might be handy, if you start raking your brain for a new solution to an old problem.

>Is there an article somewhere detailing this topic, and also
>explaining how other semi-advanced concepts could be used?

I would check https://Mathforum.org.


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Graham C
Member since Feb-5-03
May-30-03, 09:24 AM (EST)
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3. "RE: Uses for factoring trinomials"
In response to message #0
 
   >I am a High School student now, and have started taking
>Algebra. I have learned several of the methods, and have
>seen how they could be used. However, I was at a loss to
>explain how factoring trinomials can be used. Not counting
>teaching/tutoring algebra, why would I need to know how to
>do this? I am not saying it is unnecessary, I would just
>like some facts.
>
>Can you list a couple of occupations that require
>familiarity with it?

Alex is right that you could get a computer to do it faster than a humen - so one answer to your question is that you might be asked to write such a program. Someone would have to.

A more general answer might lie in statistical analysis: if you have a series of results (say of the incidence of a kind of cancer) relating to three potentially relevant conditions, trinomial expressions would arise and you might need to factor them in the process of establishing the relative importance of the three conditions.

But I am in general agreement with Rich and Alex on their other points.

Also you might consider that if it hadn't been useful or interesting to someone, no-one would have developed the procedure in the first place.


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CSpeed
Member since Feb-19-03
Jun-02-03, 10:31 AM (EST)
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4. "RE: Uses for factoring trinomials"
In response to message #0
 
   Eigenvectors and Eigenvalues rely pretty heavily on factoring poly-nomials. This is an essential part of differential equations which is an essential part of fluid mechanics and aerodynamics.

I could probably come up with a hundred examples of Engineering problems that end up with the student factoring a polynomial. It is usually a small step in a very large problem, and doesn't always need to be done. Of course, it is nice to know that if I can get something down to a trinomial, I can solve it from there. I know that you were asking for real world examples, but the problems in engineering textbooks are pretty close.

200 years ago, people weren't as smart (in general) as we are now. This isn't a lack of knowledge, I'm talking about the ability to reason through and solve problems. We are smarter because we hone our logical reasoning skills with things like math, specifically algebra.

I agree with alexb. Questions like this seem to be asking us what the point of factoring polynomials (and math in general) is, almost like we have to justify the existence of what most us that frequent this website consider to be a lovely subject.

My $.02

--CS


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alexb
Charter Member
984 posts
Jun-03-03, 02:01 PM (EST)
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5. "RE: Uses for factoring trinomials"
In response to message #4
 
   >200 years ago, people weren't as smart (in general) as we
>are now. This isn't a lack of knowledge, I'm talking about
>the ability to reason through and solve problems.

I am not sure about that. I do not believe the brain changed significantly in the last 2000 years, not to talk of the paltry 200.

Assume we talk in terms of constructing and working with decision trees. 2-3 steps ahead is the limit of an average person today as it was in the Greek time.

>We are
>smarter because we hone our logical reasoning skills with
>things like math, specifically algebra.

It's a proven statistical fact that most of the modern day executives do not use mathematics. Their business skills either innate or have been honed elsewhere.


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CSpeed0001
Member since Feb-19-03
Jun-05-03, 11:28 AM (EST)
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6. "RE: Uses for factoring trinomials"
In response to message #5
 
   Much as I hate to argue with the big guy...

>I am not sure about that. I do not believe the brain changed
>significantly in the last 2000 years, not to talk of the
>paltry 200.
>
>Assume we talk in terms of constructing and working with
>decision trees. 2-3 steps ahead is the limit of an average
>person today as it was in the Greek time.

Children are learning more now than they ever have. I'm sure that part of this is due to us collectively becoming better teachers, but I don't think this accounts for all of it. I would consider the ability to learn new concepts to be part of intelligence.

>It's a proven statistical fact

What's a "proven statistical fact"? I didn't know there was such a thing.

>that most of the modern day
>executives do not use mathematics. Their business skills
>either innate or have been honed elsewhere.

They might not use mathmetics (I think people use math more than they realise), but they might use the same sort of problem solving skills that they learned in math. An example of this would be reducing a complicated task into a smaller, more managable series of tasks. It's possible to learn this other ways, but math is probably the most universal. I believe constructing a flow chart relies heavily on mathematical thinking, and anyone who's ever had to give a presentation has had to do this to some extent (especially when using a program like Powerpoint.)

I don't believe everyone uses math, but I do believe everyone uses the logical reasoning and algorithmic thinking that math teaches.

--CS


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Matthew
guest
Jun-12-03, 02:03 PM (EST)
 
7. "RE: Uses for factoring trinomials"
In response to message #6
 
   > (I think people use math more than they realise)

I agree with this statement. I have used algebraic methods even before I started algebra. I see how the more basic things I am learning are useful. However, I have tried and failed to see how factoring trinomials can be useful to me.

> I believe constructing a flow chart relies heavily on mathematical
> thinking, and anyone who's ever had to give a presentation has had
> to do this to some extent (especially when using a program like
> PowerPoint.)

I have learned (and am learning) this same "mathematical thinking" from the game of chess. Should chess be a required course in high school because it teaches mathematical thinking? If not, this is not a valid argument for making Algebra a required course.

Matthew


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Matthew
guest
Jun-12-03, 02:03 PM (EST)
 
8. "RE: Uses for factoring trinomials"
In response to message #4
 
   >I could probably come up with a hundred examples of
>Engineering problems that end up with the student factoring
>a polynomial. It is usually a small step in a very large
>problem, and doesn't always need to be done. Of course, it
>is nice to know that if I can get something down to a
>trinomial, I can solve it from there. I know that you were
>asking for real world examples, but the problems in
>engineering textbooks are pretty close.

What percentage of high school students become engineers? Is learning to factor trinomials a waste of all the other students time?

Matthew


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Matthew
guest
Jun-12-03, 02:03 PM (EST)
 
9. "RE: Uses for factoring trinomials"
In response to message #4
 
   >I agree with alexb. Questions like this seem to be asking
>us what the point of factoring polynomials (and math in
>general) is, almost like we have to justify the existence of
>what most us that frequent this website consider to be a
>lovely subject.

I am sorry if my question offended anybody.

I agree that math, and even algebra are "lovely subjects" if a person is in to that kind of thing. It is a wonderful hobby that is also a useful tool to people in certin professions.

However, I do not have this as a hobby. My hobbies are:
Piano
Soccer
Boy Scouts
Chess
Web page design

All of which I think are lovely subjects, and would be happy to justify the existence of them to any person interisted enough to ask.

If anybody is uncomfortable justifying the existance of the process of factoring trinomials, please accept my appology. And, rember, nobody is requiring you to.

Matthew


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Matthew
guest
Jun-12-03, 02:03 PM (EST)
 
10. "RE: Uses for factoring trinomials"
In response to message #0
 
   I want to summarize what I understand was said above.

RicBrad says the following professions all require familiarity with factoring trinomials:
engineer
scientist
economist
mathematician
computer programmer

alexb says that by the time I enter the work force no profession will require this skill, but there are an infinite number of types of practical problems that can be solved more easily by factoring trinomials, and not knowing this skill limits my creativity.

Graham C adds statistical analyst to the list of professions, and gives an example.

CSpeed describes how an engineer might use this process.

alexb posts again, saying people weren't so dumb a long time ago, and says business executives don't use math.

CSpeed0001 says people use math more than they realize, but more than that they learn logical reasoning and algorithmic thinking from math.

Did I miss anything pertinent?

Matthew


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