Let's start by finding both [tex]\( p(x) \)[/tex] and [tex]\( q(x) \)[/tex].
Given:
[tex]\[ p(x) = x + 3 \][/tex]
[tex]\[ q(x) = x - 2 \][/tex]
We want to find the value of [tex]\( p(x) \cdot q(x) \)[/tex].
First, let's choose a value for [tex]\( x \)[/tex]. In this case, let's use [tex]\( x = 4 \)[/tex].
1. Calculate [tex]\( p(4) \)[/tex]:
[tex]\[
p(4) = 4 + 3 = 7
\][/tex]
2. Calculate [tex]\( q(4) \)[/tex]:
[tex]\[
q(4) = 4 - 2 = 2
\][/tex]
Now, we need to find the product [tex]\( p(4) \cdot q(4) \)[/tex]:
[tex]\[
p(4) \cdot q(4) = 7 \cdot 2 = 14
\][/tex]
Thus, the value of [tex]\( p(x) \cdot q(x) \)[/tex] when [tex]\( x = 4 \)[/tex] is [tex]\( 14 \)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{14} \][/tex]
