The Zero Product Property Quick Check

Question

1 of 51 of 5 Items
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 .

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, 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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page 14 of 14

Answer 1

To determine whether Oliver's work is accurate, we need to analyze the work he completed with the Zero Product Property for the equation \((x+3)(x+4)=0\).

Using the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must equal zero. Thus, we can set each factor equal to zero:

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

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

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

Now, let's evaluate Oliver's table from the question:

• He has \(x−3=0\) listed, which is incorrect because it should be \(x + 3 = 0\).
• He also has \(x + 4 = 0\), which is correct.
• The found solutions in his work (i.e., \(x=3\) and \(x=-4\)) are also incorrect because he supposedly wrote \(x = 3\), which should have been \(x = -3\).

Given the analysis, the correct response to whether Oliver’s work is accurate is:

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