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September 17th, 2014, 09:13 PM   #1
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Why did this change from positive to negative

I feel like I missed something on a basic level. In the book it is shown that $\displaystyle \mathbf{{\color{Red}{k^3-1 }}}$ becomes $\displaystyle \mathbf{{\color{Red}{k^3+1 }}}$ when put into a long division style problem. Why? Also trying to start a trend here, use some words and what not, the single equation responses with no explanation and minor steps skipped don't help me. It's usually the minor step that I need to see for that type of explanation to work. Thanks.
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September 17th, 2014, 09:23 PM   #2
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That's an error. It should still be $k^3-1$.

You can check, by multiplying the solution by $(k-1)$

$$(k^2+k+1 + \frac2{k-1})(k-1) = k^3 -k^2 + k^2 - k + k - 1 + 2 = k^3 +1$$

$$(k^2 + k + 1)(k - 1) = k^3 - k^2 + k^2 - k + k -1 = k^3 -1$$
as required.
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September 17th, 2014, 10:27 PM   #3
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That's funny. I was confused all over the place with that one.
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change, negative, positive

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