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Use the table to answer the question.

(x+3)(x+4)=0x−3=0x+4=0x=3x=−4While 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 .

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 .

1 answer

To determine if Oliver's work on the equation \((x+3)(x+4) = 0\) is accurate, let's analyze 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 be zero. Therefore, to solve \((x+3)(x+4) = 0\), we set each factor equal to zero:

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

Solving these equations gives us:

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

Now, let's examine the statements regarding Oliver's work.

  • The statement "No, x−3=0 in the second row should be x+3=0" indicates a correction to the incorrect setup of the first factor. This is accurate because it points out that Oliver wrote \(x - 3 = 0\) instead of \(x + 3 = 0\).

Considering these points, we can conclude that Oliver's work is indeed not accurate due to the error in setting the factors equal to zero. Thus, the correct response is:

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