I wish I understood my own work

I obviously spent a lot of time on this last year, but what it really means escapes me now. I am so burnt out on math that I can't even understand my own stuff. Remainder theorem wiki. .I suppose it is just some strange thought which got memorialised because I wanted to make the LaTeX of something. It seems interesting anyway. On top of that, I got the last row in column 1 wrong. It doesn't even make sense to me and I made this table. Most likely, just to make a table.

\begin{array}{|c|c|c||c|c||c||} \hline \pm \delta v &V & \overbrace{R}^{Remainder} & R+1 & \sqrt{R+1} & \sqrt{R+1}-1 \\ \hline \ \ 0&0&0&0&0&-1\\ -1&1&3&4&2&1\\ -2&2&8&9&3&2\\ -3&3&15&16&4&3\\ -4&4&24&25&5&4\\ -5&5&35&36&6&5\\ -6&6&-1&0&0&-1\\ -7&7&0&1&1&0\\ -8&8&3&4&2&1\\ -9&9&8&9&3&2\\ -10&10&15&16&4&3\\ -11&11&24&25&5&4\\ -12&12&35&36&6&5\\ -13&13&48&49&7&6\\ \hline & \begin{array}{c | c} if \ v=1 & (x+5)(x+7)=x^2+12x+35 \\ \hline then: & remainder\ of\ \frac{(x+5)(x+7)}{(x+5+\delta v)}=3 \\ \hline \end{array} &&&&(\delta v)^2-1=R\\ \hline & \copyright (2009)Mohr's\ Remainder\ Theorem\\ \hline \end{array}

To be consistent above is the LaTeX.


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