To determine [tex]\((p + q)(2)\)[/tex], we'll need to follow these steps:
1. Identify the values of [tex]\(p(2)\)[/tex] and [tex]\(q(2)\)[/tex] from their respective tables.
- From the table for [tex]\(p(x)\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & p(x) \\
\hline
4 & -1 \\
\hline
2 & 3 \\
\hline
-3 & 2 \\
\hline
\end{array}
\][/tex]
We see that [tex]\( p(2) = 3 \)[/tex].
- From the table for [tex]\(q(x)\)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & q(x) \\
\hline
4 & 1 \\
\hline
2 & -2 \\
\hline
-3 & 5 \\
\hline
\end{array}
\][/tex]
We see that [tex]\( q(2) = -2 \)[/tex].
2. Calculate [tex]\( p(2) + q(2) \)[/tex]:
[tex]\[
p(2) + q(2) = 3 + (-2) = 3 - 2 = 1
\][/tex]
So, [tex]\((p + q)(2)\)[/tex] is:
[tex]\[
(p + q)(2) = 1
\][/tex]
Thus, the final result is [tex]\(\boxed{1}\)[/tex].
