The Zero Product Property Quick Check

Question

2 of 52 of 5 Items

Question
Based on the Zero Product Property, which of the following statements must be true about the quadratic equation (2x−3)(x+2)=0?(1 point)
Responses

No values of x will make the function equal 0.
No values of x will make the function equal 0.

Both factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.
Both factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

Neither of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis or left parenthesis x plus 2 right parenthesis , must equal 0 for the entire function to equal 0.

At least one of the factors, (2x−3) or ​(x+2), must equal 0 for the entire function to equal 0.

Answer 1

The Zero Product Property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

For the quadratic equation \((2x−3)(x+2)=0\), according to this property, at least one of the factors \((2x−3)\) or \((x+2)\) must equal 0 for the equation to hold true.

Therefore, the correct statement is:

At least one of the factors, (2x−3) or (x+2), must equal 0 for the entire function to equal 0.