To find [tex]\((p+q)(2)\)[/tex], we first need to look at the values of [tex]\( p(x) \)[/tex] and [tex]\( q(x) \)[/tex] at [tex]\( x = 2 \)[/tex].
From the table for [tex]\( p(x) \)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $p(x)$ \\
\hline
4 & -1 \\
\hline
2 & 3 \\
\hline
-3 & 2 \\
\hline
\end{tabular}
\][/tex]
we see that [tex]\( p(2) = 3 \)[/tex].
From the table for [tex]\( q(x) \)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $q(x)$ \\
\hline
4 & 1 \\
\hline
2 & -2 \\
\hline
-3 & 5 \\
\hline
\end{tabular}
\][/tex]
we see that [tex]\( q(2) = -2 \)[/tex].
Now, we find [tex]\( (p+q)(2) \)[/tex] by adding these two values:
[tex]\[
(p+q)(2) = p(2) + q(2) = 3 + (-2) = 1
\][/tex]
Therefore,
[tex]\[
(p+q)(2) = 1
\][/tex]
