### 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
\hline
\end{array}


To be consistent above is the LaTeX.