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Originally Posted by sanddrag
Can you factor (x+1) out of (x^3+1)? I would think you can, but I'm uncertain of what the other factor(s) is/are. How do you determine this?
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Yes, you can. The factor theorem states that if you have a polynomial f(x), where f(a) = 0, then (x-a) is a factor of f(x).
In this case f(-1) = (-1)^3 + 1 =0, hence (x+1) is a factor.
By long division, you can see that (x^3+1) = (x^2 - x + 1)(x + 1)
This is also an example of the "Sum of Cubes"; (x^3 + y^3) = (x + y)(x^2 - xy + y^2)