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, 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 .

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

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 .

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 .

Answer 1

To analyze whether Oliver's work is accurate, let's carefully review the steps given in the table and the correct application of the Zero Product Property.

Starting from the equation:

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

According to the Zero Product Property, for the product of two factors to equal zero, at least one of the factors must be equal to zero:

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

Solving these equations:

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

Oliver’s table suggests:

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

From the table, there is a mistake in the first row where it states \(x - 3 = 0\) instead of \(x + 3 = 0\).

Therefore, the correct root from the first factor should be \(x = -3\), not \(x = 3\).

So based on the analysis, the accurate response to the question is:

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