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

Question

?(1 point)
Responses

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

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

Neither of the factors, (2x−3)
nor ​(x+2)
, must equal 0 for the entire function to equal 0.
Neither of the factors, left parenthesis 2 x minus 3 right parenthesis nor 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

Based on the Zero Product Property, 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.

This is because the property states that if the product of two factors equals zero, then at least one of the factors must be equal to zero. In this case, setting either (2x−3) or (x+2) to zero will give solutions for x that satisfy the equation (2x−3)(x+2)=0.