Can Factoring Be Considered a Skill?

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  • Thread starter Thread starter mathland
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SUMMARY

The discussion centers on the concept of factoring, specifically whether it can be classified as a skill. Participants agree that understanding mathematical techniques, such as logarithmic functions and division, is essential for effective factoring. Dan demonstrates the factoring of 343 using division by 7 and expresses that logarithms are unnecessary for this process. The consensus leans towards recognizing factoring as a skill rather than merely a trick.

PREREQUISITES
  • Understanding of basic arithmetic operations, particularly division.
  • Familiarity with logarithmic functions, specifically log base 7.
  • Knowledge of exponentiation and square roots.
  • Ability to manipulate algebraic expressions.
NEXT STEPS
  • Research the properties of logarithms and their applications in factoring.
  • Explore advanced factoring techniques, including polynomial factoring.
  • Learn about the relationship between exponents and roots in algebra.
  • Study mathematical problem-solving strategies to enhance factoring skills.
USEFUL FOR

Students, educators, and anyone looking to improve their mathematical skills, particularly in factoring and algebraic manipulation.

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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