Question

7. Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (5x + 1) (x − 8) = 0?
A) No values of x will make the left side of the equation equal 0.
B) Neither of the factors, (5x + 1) or (x − 8), must equal 0 for the left side of the equation to equal 0.
C) At least one of the factors, (5x + 1) or (x − 8), must equal 0 for the left side of the equation to equal 0.

8. While using the Zero Product Property to find the solutions for the quadratic equation (x − 2) (x − 9) = 0, a student completed the work below. Is the student's work correct?
(x − 2) (x − 9) = 0 original equation
Solution #1: x − 2 = 0
x = 2
Solution #2: x + 9 = 0
x = −9
A) Yes, the student answered the problem correctly.
B) No, there should be a solution #3.
C) No, x + 2 = 0 should have been used to find solution #1.
D) No, x − 9 = 0 should have been used to find solution #2.

Answer 1

7. The correct answer is **C)** At least one of the factors, (5x + 1) or (x − 8), must equal 0 for the left side of the equation to equal 0. This is based on the Zero Product Property, which states that if a product of two factors equals zero, then at least one of the factors must be zero.

8. The correct answer is **D)** No, x − 9 = 0 should have been used to find solution #2. The student's first solution is correct (x - 2 = 0 gives x = 2), but the second solution incorrectly states x + 9 = 0 instead of correctly using x - 9 = 0, which would yield x = 9.