Factorising x^3 + 216 to Include (x + 6)

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Homework Help Overview

The discussion revolves around the factorization of the polynomial expression x^3 + 216, specifically to include the factor (x + 6). Participants are exploring methods to achieve this factorization within the context of polynomial algebra.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss polynomial division as a potential method and reference the sum of cubes formula. There is also mention of long division and the challenges of recalling these methods after a break from study.

Discussion Status

The conversation is active, with various approaches being suggested, including polynomial division and the application of the sum of cubes formula. Some participants are reflecting on their understanding and recalling techniques, indicating a collaborative effort to clarify the problem.

Contextual Notes

There appears to be some uncertainty regarding the application of polynomial division and the sum of cubes, as well as a recognition of the need to refresh knowledge after a break from the material.

Alkatran
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I need to factorise x^3 + 216 to include (x+6):

(x + 6) \ (x^3 + 216) (lim where x approaches -6)

I broke it down to (x + 6i)(x^2 - 36i) ... but that's no good.
 
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Well, shouldn't polynomial division work fine?
 
Remember

[tex]X^3 + Y^3 = (X+Y)(X^2-XY+Y^2)[/tex]
 
He has

[tex]\frac{x+6}{x^3 + 216}[/tex]

[tex]\frac{x+6}{x^3 + 6^3}[/tex]
 
I got it fine before I even came back. I was trying to remember how to do long division and the cube rule that you guys posted. The start of the year, still getting restarted...
 

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