Question

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 Olivers work accurate?

A: No x+4 = 0 in the second row should be x- - 4 = 0

B: No, x - 3 = 0 in the second row should be x + 3 = 0

C: Yes, the work is accurate.

D: No, she should have a third column where he should set x = 0.

Answer 1

To evaluate Oliver's work with the quadratic equation \((x+3)(x+4) = 0\) using the Zero Product Property, we need to set each factor equal to zero:

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

Now, let's solve these equations:

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

Now, let's assess each of the options provided:

A: "No, \(x+4 = 0\) in the second row should be \(x - - 4 = 0\)."
This is inaccurate; the equation is correct as is.

B: "No, \(x - 3 = 0\) in the second row should be \(x + 3 = 0\)."
This is inaccurate; \(x + 3 = 0\) is indeed correct.

C: "Yes, the work is accurate."
If the work shows \(x + 3 = 0\) and \(x + 4 = 0\) correctly, this is true.

D: "No, she should have a third column where she should set \(x = 0\)."
This is not necessary for solving the equation using the Zero Product Property. Setting each factor to zero is sufficient.

Based on this analysis, the best answer is:

**C: Yes, the work is accurate.**

If Oliver correctly set the factors as \(x + 3 = 0\) and \(x + 4 = 0\), then the work is accurate.