The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be equal to zero. This property can be applied only when the equation is in the form of a product equal to zero.
Let's analyze each option:
Option 1: \((x−2)(x+3)=7\)
- This is not in the form of a product equal to zero, so the Zero Product Property cannot be used.
Option 2: \(x(x+3)=0\)
- This is in the form of a product equal to zero (\(x \cdot (x + 3) = 0\)). The Zero Product Property can be applied here to find the zeros.
Option 3: \((x+3)^2−1=0\)
- This is not in the form of a product equal to zero. It is an equation that can be solved by other means, such as factoring or using the quadratic formula.
Based on this analysis, the only option where the Zero Product Property can be used is:
Option 2: \(x(x+3)=0\)
1 answer