The Zero Product Property can only be applied to equations that are already in the form of a product equal to zero, i.e., in the form \(A \cdot B = 0\).
Let's analyze each option:
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Option 1: \((x−2)(x+3)=7\)
This equation is not set equal to zero, so the Zero Product Property cannot be applied directly. -
Option 2: \(x(x+3)=0\)
This equation is already in the form of a product equal to zero. We can apply the Zero Product Property here, which states that if \(A \cdot B = 0\), then either \(A = 0\) or \(B = 0\). Thus, we can set \(x = 0\) or \(x + 3 = 0\) (leading to \(x = -3\)) to find the zeros. -
Option 3: \((x+3)^2−1=0\)
This equation is not in a product form. It involves a quadratic expression set equal to zero, but it would need to be factored first before applying the Zero Product Property.
Therefore, the only option in which the Zero Product Property can be used directly is Option 2: \(x(x+3)=0\).
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