Question

(2x + 4)(3x - 2) = 0

According to the zero product property, this equation is true if and only if:

A. (2x + 4) = 0 or (3x - 2) = 0
B. (2x - 4) = 0 or (3x + 2) = 0
C. (2x + 4) = 0 and (3x - 2) = 0
D. (2x - 4) = 0 and (3x + 2) = 0

Answer 1

The correct answer is A: (2x + 4) = 0 or (3x - 2) = 0 since at least one of the factors must equal zero for their product to equal zero.

Step-by-step explanation:

According to the zero product property, a product of factors equals zero if and only if at least one of the factors equals zero. Therefore, when we have an equation in the form (2x + 4)(3x - 2) = 0, we can say that either (2x + 4) equals zero, or (3x - 2) equals zero. This corresponds to choice A: (2x + 4) = 0 or (3x - 2) = 0. Each equation needs to be solved for x to find the specific values of x that make the equation true.