Algebra Calculators: Expanding, Factoring & Finding Roots

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Discussion Overview

The discussion revolves around the use of algebra calculators for expanding, factoring, and finding roots of equations. Participants explore the capabilities of various calculators, the importance of understanding algebraic processes, and the implications of relying on technology for mathematical tasks.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about calculators that can perform symbolic calculations, such as expanding and factoring expressions like (x+3)(2x-9)(x+4).
  • Others mention specific models, like the TI80 and TI89 series, that can perform these operations and suggest using the "Expand" function.
  • There are concerns expressed about the potential negative impact of calculators on mental math skills, with one participant sharing a personal experience of becoming reliant on calculators to the detriment of their mental arithmetic abilities.
  • Some participants argue that while calculators can be useful for complex problems, it is still important to learn and practice the underlying mathematical concepts.
  • One participant notes that MATLAB can also perform symbolic math, suggesting alternative software options for those interested.

Areas of Agreement / Disagreement

Participants generally agree that calculators can be helpful for certain tasks, but there is significant disagreement regarding their impact on learning and mental math skills. Some advocate for using calculators, while others caution against over-reliance on them.

Contextual Notes

Participants express varying opinions on the effectiveness and practicality of calculators, with some highlighting limitations such as screen size and readability for complex equations. The discussion reflects a range of experiences and attitudes towards the use of technology in mathematics.

Who May Find This Useful

This discussion may be of interest to students learning algebra, educators considering the role of calculators in teaching, and professionals in fields that require mathematical calculations.

JimmyJockstrap
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Is there calculators you can type in eg.

(x+3)(2x-9)(x+4)=y and it can expand and factorise, vice versa for you?

or would you just use a graph calculator to find the roots?
 
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Yes, there are calculators that will do "symbolic" calculations. The TI80 series comes to mind. But it is real good idea to learn how to do them yourself and not depend on calculators!
 
That's not even a hard thing to break down and fool around with.

It gets way harder than that. And even then, do it yourself and test it to see if it's correct. Put some time into it. :smile:
 
JimmyJockstrap: (x+3)(2x-9)(x+4)=y and it can expand and factorise, vice versa for you?

Sure, put it into the TI89 and use the "Expand" key and get: 2X^3 + 5X^2-39X-108.
 
my experience (admittedly early in the algebraic calculator time frame) was that the equations displayed on the limited screen were so hard to decipher, that it was only practical to use on simple equations, but then you should not need the calculator to do the the simple stuff.
 
The screen is not all that good, but if you are interested in things like:

(1+\sqrt5)^6 = 576 +256\sqrt5, then you get the answer right away.
 
remark: calculators are evil. they make you dumber.

think about it, if riding in a car and sitting in front of the tv with a remote makes you fat and lazy and slow, what do you think it does to your brain to use a calculator?

the action is very fast too. one summer i used a calculator to change policy premiums at an insurance firm, and out of habit when i ahd a simple problem to do, instead of adding up the numbers in my head i used the calculator.

by th end oif the summer i could not do squat in my head after leaving the firm for quite a while. and i was a star at doing mental math. so beware. if you laugh at the fat kid who sits in the stands eating a big pizza while you are playing basketball, well mentally that is you, if you are using a calculator, and the fat is in your brain.

so there. now try to enjoy your calculator.
 
Halls of Ivy: Yes, there are calculators that will do "symbolic" calculations. The TI80 series comes to mind. But it is real good idea to learn how to do them yourself and not depend on calculators!
__________________
Of course, I was not supposing it was better to buy the TI-89 and learn that in order to do simple Algebra!
 
mathwonk said:
remark: calculators are evil. they make you dumber.

think about it, if riding in a car and sitting in front of the tv with a remote makes you fat and lazy and slow, what do you think it does to your brain to use a calculator?

the action is very fast too. one summer i used a calculator to change policy premiums at an insurance firm, and out of habit when i ahd a simple problem to do, instead of adding up the numbers in my head i used the calculator.

by th end oif the summer i could not do squat in my head after leaving the firm for quite a while. and i was a star at doing mental math. so beware. if you laugh at the fat kid who sits in the stands eating a big pizza while you are playing basketball, well mentally that is you, if you are using a calculator, and the fat is in your brain.

so there. now try to enjoy your calculator.

At the same time I don't want to spend 20 minutes working out an integral I know I can do when a calculator will give me the same answer in seconds. I'm a physicist, not a mathematician. I don't need to work out every problem. I just need to know that I'm capable of doing it.
 
  • #10
If you have MATLAB on your computer, it does symbolic math too
 

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