Let's verify Oliver's work concerning the equation \((x+3)(x+4) = 0\) using the Zero Product Property.
According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we have:
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Set each factor equal to zero: \[ x + 3 = 0 \quad \text{or} \quad x + 4 = 0 \]
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Solving each equation:
- From \(x + 3 = 0\): \[ x = -3 \]
- From \(x + 4 = 0\): \[ x = -4 \]
Thus, the solutions for \((x+3)(x+4) = 0\) are \(x = -3\) and \(x = -4\).
Now let's review Oliver's work:
- He listed \(x - 3 = 0\) which is incorrect because it corresponds to a different equation.
- He correctly found \(x + 4 = 0\) leading to \(x = -4\).
- He stated \(x = 3\) which is also incorrect.
Oliver's solutions for \(x\) should be \(x = -3\) and \(x = -4\). Therefore, his work is not accurate.