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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, 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.

1 answer

To evaluate Oliver's work, we need to review the given equation and its factors:

The original equation is \((x+3)(x+4) = 0\).

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

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

From the steps:

  • The second equation listed directly in the table, \(x - 3 = 0\), is not relevant to these factors. It appears to be an error.
  • The factorization is correct, but the conclusions derived from \(x - 3 = 0\) do not follow from the factors of the equation \((x+3)(x+4) = 0\).

Therefore, the option that accurately critiques Oliver's work is:

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