How can -x^3 + 27 be factored?

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Homework Help Overview

The problem involves factoring the expression -x^3 + 27, which is related to polynomial factorization, specifically focusing on the difference of cubes.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to factor the expression. Some participants provide formulas related to the sum and difference of cubes, while others note the specific form of the expression as fitting the difference of cubes.

Discussion Status

Participants have shared relevant formulas and identified the expression's structure. There appears to be a productive direction as some participants have successfully connected the problem to the provided formulas, although no explicit consensus on the factoring process has been reached.

Contextual Notes

The original poster has indicated a lack of initial attempts at factoring, and some participants have noted the specific challenge posed by the negative coefficient of x^3.

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Homework Statement


factor -x^3 + 27


Homework Equations





The Attempt at a Solution



Nothing, I have no idea how to factor it.
 
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Here are a couple of formulas for you:
a3 + b3 = (a + b)(a2 - ab + b2)
a3 - b3 = (a - b)(a2 + ab + b2)
 
Mark44 said:
Here are a couple of formulas for you:
a3 + b3 = (a + b)(a2 - ab + b2)
a3 - b3 = (a - b)(a2 + ab + b2)

I tried those. My main problem is the -x^3.
 
You've got 3^3-x^3. That fits the second formula Mark44 gave you.
 
2 seconds on physics forum and I found what I'm after. Thanks very much.
 
Sorry we took so long!
 

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