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September 17th, 2014, 09:13 PM  #1 
Senior Member Joined: Aug 2014 From: Mars Posts: 101 Thanks: 9  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 $\displaystyle \mathbf{{\color{Red}{k^31 }}}$ 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.

September 17th, 2014, 09:23 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,600 Thanks: 2588 Math Focus: Mainly analysis and algebra 
That's an error. It should still be $k^31$. You can check, by multiplying the solution by $(k1)$ $$(k^2+k+1 + \frac2{k1})(k1) = k^3 k^2 + k^2  k + k  1 + 2 = k^3 +1$$ While $$(k^2 + k + 1)(k  1) = k^3  k^2 + k^2  k + k 1 = k^3 1$$ as required. 
September 17th, 2014, 10:27 PM  #3 
Senior Member Joined: Aug 2014 From: Mars Posts: 101 Thanks: 9 
That's funny. I was confused all over the place with that one.


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