Use the table to answer the question.

Question

Option 1 (x−2)(x+3)=7

Option 2 x(x+3)=0

Option 3 (x+3)^2−1=0

It is only possible to use the Zero Product Property on one of the options in this table. Which option can the Zero Product Property be used on to find the zeros of the function?

(1 point)
Option

Answer 1

The Zero Product Property states that if two factors multiplied together equal zero, then at least one of the factors must be equal to zero. This property can only be directly applied when the equation is in the form of a product set equal to zero.

Let's analyze each option:

1. Option 1: \((x−2)(x+3)=7\)
   This is not equal to zero, so the Zero Product Property cannot be used here.

2. Option 2: \(x(x+3)=0\)
   This equation is already in the form where the product equals zero, so the Zero Product Property can be applied.

3. Option 3: \((x+3)^2−1=0\)
   This is not a product equal to zero; it's a quadratic equation that can be factored, but does not directly allow for the Zero Product Property as it's not in that form.

Therefore, the option where the Zero Product Property can be used is:

Option 2 \(x(x+3)=0\)