How can -x^3 + 27 be factored?

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SUMMARY

The expression -x^3 + 27 can be factored using the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a is 3 and b is x, leading to the factorization -x^3 + 27 = -(x - 3)(x^2 + 3x + 9). The discussion highlights the importance of recognizing the structure of cubic expressions for effective factoring.

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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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