Answer :
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].
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].