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+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.
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 .
The Zero Product Property states that if the product of two expressions is zero, then at least one of the expressions must be zero. In the quadratic equation (x+3)(x+4) = 0, we have two expressions (x+3) and (x+4) multiplied together to give zero.
The correct application of the Zero Product Property involves setting each factor equal to zero separately and solving for x:
1. x + 3 = 0 => x = -3
2. x + 4 = 0 => x = -4
Given the choices, the correct statement is:
Yes, the work is accurate.
Oliver correctly set each factor equal to zero and solved for x. The errors provided in the other options are not present in Oliver's work:
- "No, x+4=0 in the second row should be x−4=0." This is incorrect because the factor is correctly stated as (x+4).
- "No, he should have a third column where he should set x=0." This is incorrect because only the two factors, x+3 and x+4, are relevant for the Zero Product Property; there's no need for a third column.
- "No, x−3=0 in the second row should be x+3=0." This is incorrect because the factor is already correctly stated as (x+3).
Therefore, if Oliver set each factor to zero and solved for x correctly, then his work is accurate.