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Use the table to answer the 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

1 answer

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 property can only be applied when the equation is set to zero.

  1. Option 1: \((x−2)(x+3)=7\)

    • This equation is equal to 7, not 0, so the Zero Product Property cannot be applied.

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

    • This equation is already set to zero. Therefore, using the Zero Product Property, we can set each factor to zero: \(x = 0\) or \(x + 3 = 0\) (which gives \(x = -3\)).

  3. Option 3: \((x+3)^2−1=0\)

    • This equation could potentially be rewritten to apply the Zero Product Property, but it first needs to be factored or rearranged. However, it's not in a direct product form.

Therefore, the only option where the Zero Product Property can be directly applied is:

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