Let's go through this step-by-step.
We are given a polynomial [tex]\( p(x) \)[/tex] written as a product of linear factors. The polynomial can be expressed as:
[tex]\[ p(x) = (x-2)(x+2)(x) \][/tex]
We need to determine if any of these factors appear twice among:
1. [tex]\( x-2 \)[/tex]
2. [tex]\( x+2 \)[/tex]
3. [tex]\( x-3 \)[/tex]
4. [tex]\( x+3 \)[/tex]
Let's identify the factors we have in our polynomial:
- The first factor is [tex]\( x-2 \)[/tex].
- The second factor is [tex]\( x+2 \)[/tex].
- The third factor is [tex]\( x \)[/tex].
On inspection:
- Factor [tex]\( x-2 \)[/tex] appears once.
- Factor [tex]\( x+2 \)[/tex] appears once.
- Factor [tex]\( x \)[/tex] appears once.
- Factors [tex]\( x-3 \)[/tex] and [tex]\( x+3 \)[/tex] do not appear at all.
Thus, we see that none of the given factors [tex]\( x-2 \)[/tex], [tex]\( x+2 \)[/tex], [tex]\( x-3 \)[/tex], or [tex]\( x+3 \)[/tex] appear more than once in the polynomial.
Therefore, the answer is:
[tex]\[ \boxed{\text{None of the given factors appear twice}} \][/tex]
