Question

Use the table to answer the question.
(x + 3)(x + 4) = 0.
x - 3 = 0 | x+4 = 0
x = 3 | x = -4

While using the Zero Product Property to find the values of x that make the quadratic equation ( x + 3) (x + 4) equals 0, Oliver completed the work provided in the table. Is Oliver's work accurate?

No, x + 4 = 0 in the second row should be x - 4 = 0.
No, he should have a third column where he should set x = 0.
Yes, the work is accurate.
No, x - 3 = 0 in the second row should be x + 3 = 0.

Answer 1

To evaluate Oliver's work accurately, let's inspect the expression given:

**(x + 3)(x + 4) = 0**

Using the Zero Product Property, we set each factor equal to zero to find the values of \(x\):

1. **x + 3 = 0** leads to \(x = -3\)
2. **x + 4 = 0** leads to \(x = -4\)

From the table you provided, it looks like there is confusion regarding the equations listed.

- The first row correctly identifies one factor as **x + 3 = 0**, which leads to **x = -3**.
- However, in the second row, instead of saying **x + 4 = 0**, it incorrectly states **x - 4 = 0**, which is incorrect.

Hence, the correct answers should be:
- From **x + 3 = 0**, you get \(x = -3\).
- From **x + 4 = 0**, you would get \(x = -4\).

Therefore, in response to your question regarding Oliver's work:

**No, x + 4 = 0 in the second row should be x - 4 = 0.** is not accurate. Instead, it should recognize that he made an error with the equation, which was supposed to be **x + 4 = 0** which leads to \(x = -4\).

So, the answer that fits your context best would be:

**No, x - 3 = 0 in the second row should be x + 3 = 0.**

You may also phrase it as: **No, his second factor should state x + 4 = 0 instead of x - 4 = 0.**

Thus Oliver's work is not accurate.