How to factor x^6-x^3 completely
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How to factor x^6-x^3 completely

[From: ] [author: ] [Date: 12-05-02] [Hit: ]
factor the GCF.You have a difference of cubes.Since a = x and b = 1, after taking the cube root of each,The quadratic cant be factored. Thats your full factorization.......
I was wondering how to completely factor that equation. My math book is very crappy and doesn't offer any help at all. Detailed answers please...

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First, factor the GCF. The GCF is x^3:

x^3(x^3 - 1)

You have a difference of cubes. The formula is:

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Since a = x and b = 1, after taking the cube root of each, we can put it into the formula:

x^3(x - 1)(x^2 + x + 1)

The quadratic can't be factored. That's your full factorization.

Does this help?

Miss Kristin

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Factor out x^3.
Now you have: x^3 (x^3 -1)
The (x^3 -1) can also be factored: The generic equation is a^3 - b^3 = (a-b)(a^2 +ab +b^2). The cube root of x^3 is x (equivalent to a in the example), and the cube root of 1 is 1(equivalent to b).
So, (x^3 -1) can be factored: (x-1)(x^2 +x +1).
The answer is x^3(x-1)(x^2 +x +1).
Hope I helped.

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x^3(x^3-1)

http://www.purplemath.com/modules/simpfa…

Great website for learning math.
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