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?(1 point)
Responses

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, 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, he should have a third column where he should set x=0.
No, he should have a third column where he should set x equals 0 .
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Answer 1

To determine if Oliver's work is accurate, we need to review the steps he's taken to solve the equation \((x+3)(x+4)=0\) using the Zero Product Property.

The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must equal 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. From \(x + 3 = 0\), we get \(x = -3\).
2. From \(x + 4 = 0\), we get \(x = -4\).

However, in Oliver's work, he wrote:

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

In this case, the first equation, \(x - 3 = 0\), is incorrect. The correct equation should indeed be \(x + 3 = 0\).

Thus, the correct solutions should have been \(x = -3\) and \(x = -4\), while Oliver mistakenly included \(x = 3\).

Therefore, the accurate response for assessing Oliver's work is:
**No, x − 3 = 0 in the second row should be x + 3 = 0.**