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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=−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

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+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 .

1 answer

To determine if Oliver's work is accurate, we need to look at the steps he provided for solving the equation \((x + 3)(x + 4) = 0\) using the Zero Product Property.

The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must equal zero.

In Oliver's table:

  • He sets \(x + 3 = 0\) leading to \(x = -3\).
  • He sets \(x + 4 = 0\) leading to \(x = -4\).

However, there seems to be a mistake in the interpretation of the previous response options you provided. The correct factors derived from the equation \((x + 3)(x + 4) = 0\) should give:

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

The option saying, “No, \(x + 4 = 0\) in the second row should be \(x - 4 = 0\)” is incorrect because it confuses the equation and the roots obtained.

So, considering the evaluation and the relevant factors, the correct answer would be:

Yes, the work is accurate.

He correctly found the values of \(x\) that solve the equation.