Use the table to answer the question

Question

________________
(x + 3)(x + 4) = 0 |
x – 3 = 0 x + 4 = 0 |
x = 3 x = -4 |
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While using the Zero Property to find the values of x that make the quadratic equation (x + 3)(x + 4) = 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?

Answer 1

Let's analyze Oliver's work in the table step by step.

The equation given is \((x + 3)(x + 4) = 0\).

According to the Zero Product Property, if the product of two factors equals zero, at least one of the factors must equal zero. Therefore, we can set each factor in the equation to zero:

1. Setting the first factor to zero: \[ x + 3 = 0 \] Solving for \(x\), we get: \[ x = -3 \]

2. Setting the second factor to zero: \[ x + 4 = 0 \] Solving for \(x\), we get: \[ x = -4 \]

Following the steps above, the solutions to the equation \((x + 3)(x + 4) = 0\) are \(x = -3\) and \(x = -4\).

Now looking at Oliver's table:

• He mentioned \(x + 4 = 0\), which correctly leads to \(x = -4\).
• However, he also stated \(x - 3 = 0\), which leads to \(x = 3\).

The factor \(x - 3\) does not correspond properly to the factors of the original equation \((x + 3)(x + 4)\). The factor \(x + 3\) should have been used, which leads to the solution \(x = -3\) instead.

In summary, Oliver's work is not accurate. The correct solutions for the equation \((x + 3)(x + 4) = 0\) are \(x = -3\) and \(x = -4\).