Use the table to answer the question.

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.