Can Factoring Be Considered a Skill?

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  • Thread starter Thread starter mathland
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Discussion Overview

The discussion revolves around the nature of factoring in mathematics, specifically whether it can be classified as a skill or a trick. Participants explore different approaches to solving a problem involving the number 343, with some suggesting logarithmic methods while others advocate for direct division and simplification.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose taking the logarithm of both sides as a method to solve the problem.
  • Others suggest that dividing 343 by 7 directly is a more straightforward approach, leading to the conclusion that 343 equals 7 cubed.
  • One participant emphasizes that logarithms are unnecessary for this problem, advocating for a more direct method of factoring.
  • There is a discussion about whether factoring should be considered a "trick" or a "skill," with at least one participant expressing disagreement with the term "trick." Another participant clarifies that they meant to refer to it as a skill instead.

Areas of Agreement / Disagreement

Participants express differing opinions on the classification of factoring, with some viewing it as a skill and others as a trick. The discussion remains unresolved regarding this classification.

Contextual Notes

There are multiple approaches to solving the problem presented, and participants have not reached a consensus on the most effective method or the terminology used to describe factoring.

mathland
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I say we take the log on both sides as step one.

Yes?
 
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log base 7 looks good, yes.

-Dan
 
The first thing I would do is start dividing 343 by 7! 343- 40(7)= 343- 280= 63= 9(7) so [math]343= 7(49)= 7(7)(7)= 7^3[/math]. [math]\sqrt{343}= 7^{3/2}[/math] so [math]7^{2n}= 7^{3/2}[/math] so [math]2n= 3/2[/math], n= 3/4.

No logarithms necessary!
 
Country Boy said:
The first thing I would do is start dividing 343 by 7! 343- 40(7)= 343- 280= 63= 9(7) so [math]343= 7(49)= 7(7)(7)= 7^3[/math]. [math]\sqrt{343}= 7^{3/2}[/math] so [math]7^{2n}= 7^{3/2}[/math] so [math]2n= 3/2[/math], n= 3/4.

No logarithms necessary!

Nicely done! It pays to know math tricks.
 
Beer soaked non sequitur ramblings follow.
mathland said:
Nicely done! It pays to know math tricks.
A man's mind stretched by a new idea can never go back to its original dimension.
 
I don't think I would consider factoring a "trick".
 
Country Boy said:
I don't think I would consider factoring a "trick".

I meant to say skill not trick.
 

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