Let's analyze the strategies used by Carla and Jordan to solve the equation [tex]\((x+1)(x-1) = 8\)[/tex].
### Carla's Method:
1. Expand the Left-hand Side:
[tex]\[
(x+1)(x-1) = x^2 - 1
\][/tex]
2. Rewrite the Equation:
[tex]\[
x^2 - 1 = 8
\][/tex]
3. Isolate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 - 1 + 1 = 8 + 1
\][/tex]
[tex]\[
x^2 = 9
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \pm \sqrt{9}
\][/tex]
[tex]\[
x = \pm 3
\][/tex]
So using Carla's method, the solutions are [tex]\(x = 3\)[/tex] or [tex]\(x = -3\)[/tex].
### Jordan's Method:
1. Attempt to Use the Zero Product Property:
The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. This means:
[tex]\[
(x+1)(x-1) = 0
\][/tex]
However, the equation given is [tex]\((x+1)(x-1) = 8\)[/tex], which is not zero. Therefore, the zero product property does not apply here. Jordan's approach cannot be used to find the solution.
### Conclusion:
Carla's strategy of expanding and solving the equation works correctly and leads to the correct solutions. Jordan's approach does not work because the zero product property can only be applied when the right-hand side of the equation is zero, which is not the case here.
Therefore, the correct answer is:
- (A) Only Carla's
