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 Olivers work accurate?
a No, x + 4 = 0 in the second row should be x - 4 = 0
b No, he should have a third column where he should set x = 0
c Yes, the work is accurate
d No, x - 3 = 0 in the second row should be x + 3 = 0

Answer 1

To evaluate Oliver's work correctly:

1. The equation \((x + 3)(x + 4) = 0\) is factored correctly.
2. According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero:

- \(x + 3 = 0\)
- \(x + 4 = 0\)

3. Solving these gives the correct solutions:
- \(x + 3 = 0 \Rightarrow x = -3\)
- \(x + 4 = 0 \Rightarrow x = -4\)

According to the table you provided, it seems there’s an error in stating:

- \(x - 3 = 0\) should actually be \(x + 3 = 0\), which provides the correct root \(x = -3\).

Therefore, the correct answer is:
**d No, x - 3 = 0 in the second row should be x + 3 = 0.**