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?

Answer 1

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−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 .

No, x+4=0 in the second row should be x−4=0.

Answer 2

To check if Oliver's work is accurate, let’s break down the solution using the Zero Product Property.

The equation given is:

\[
(x + 3)(x + 4) = 0
\]

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

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

Now we can solve each equation:

1. From \( x + 3 = 0 \):
\[
x = -3
\]

2. From \( x + 4 = 0 \):
\[
x = -4
\]

So the correct solutions for the equation \( (x + 3)(x + 4) = 0 \) are \( x = -3 \) and \( x = -4 \).

In Oliver's work, the solutions listed are:
- From \( x - 3 = 0 \): \( x = 3 \)
- From \( x + 4 = 0 \): \( x = -4 \)

There is an error in this work. The correct solutions should include \( x = -3 \) from \( x + 3 = 0 \) instead.

Thus, Oliver's work is not accurate. The correct values of \( x \) that make the equation true are \( x = -3 \) and \( x = -4 \).

Answer 3

Based on the evaluation of Oliver's work, the correct response is:

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

This is the correct choice because one of the factors \( x + 3 = 0 \) was incorrectly stated as \( x - 3 = 0 \) in his work, leading to an incorrect solution of \( x = 3 \). The correct factorization should have involved \( x + 3 \).