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?(1 point)
Responses

No, x+4=0
in the second row should be x−4=0
.
No, x plus 4 equals 0 in the second row should be x minus 4 equals 0 .

Yes, the work is accurate.
Yes, the work is accurate.

No, x−3=0
in the second row should be x+3=0
.
No, x minus 3 equals 0 in the second row should be x plus 3 equals 0 .

No, he should have a third column where he should set x=0
.

Answer 1

To analyze Oliver's work, we need to apply the Zero Product Property correctly. The equation given is:

\[ (x + 3)(x + 4) = 0 \]

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 set each factor equal to zero:

1. \(x + 3 = 0\)
2. \(x + 4 = 0\)

From these equations, we can solve for \(x\):

1. For \(x + 3 = 0\): \[ x = -3 \]
2. For \(x + 4 = 0\): \[ x = -4 \]

Oliver's work shows:

1. \(x - 3 = 0\) (this is incorrect; he should have \(x + 3 = 0\))
2. \(x + 4 = 0\) (this part is correct)
3. Solutions found: \(x = 3\) (incorrect; it should be \(x = -3\)) and \(x = -4\) (this part is correct).

From the options provided, we can see that the correct conclusion is that Oliver made an error. Specifically, in the second row, he should have had \(x + 3 = 0\) instead of \(x - 3 = 0\), and the solution for \(x\) should show \(x = -3\) instead of \(x = 3\).

So the correct answer is:

No, \(x - 3 = 0\) in the second row should be \(x + 3 = 0\).