The Zero Product Property Quick Check

Question

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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+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 .

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 .
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Answer 1

To analyze Oliver's work using the Zero Product Property for the equation \((x + 3)(x + 4) = 0\):

1. According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must equal zero.
2. This means we should set each factor to zero separately:
   • \(x + 3 = 0\) → \(x = -3\)
   • \(x + 4 = 0\) → \(x = -4\)

Now, looking at the work recorded in the table:

• The first row \(x - 3 = 0\) is incorrect since that does not correspond to any of the factors from the equation.
• The second row \(x + 4 = 0\) is correct but was expected to have \(x + 3 = 0\) in the first row instead.

Based on this evaluation, the correct assessment is:

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

Therefore, the correct response to the question is:

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