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.

Answer 1

To analyze Oliver's work, we need to apply the Zero Product Property correctly to the equation \((x+3)(x+4) = 0\).

1. According to the Zero Product Property, if the product of two factors equals zero, at least one of the factors must equal zero. Therefore, we set each factor to zero:

   • \(x+3 = 0\)
   • \(x+4 = 0\)

2. Solving these equations, we get:

   • From \(x+3=0\), we find \(x = -3\).
   • From \(x+4=0\), we find \(x = -4\).

3. It appears that in the table, Oliver incorrectly stated one of the equations. The line that mentions \(x−3=0\) is not from the original set of factors from \((x+3)(x+4)\). Instead, it should have the equation \(x+3=0\).

Given the provided options, the correct answer is: No, x−3=0 in the second row should be x+3=0.