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 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. 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. No values of x will make the function equal 0. No values of x will make the function equal 0. At least one of the factors, (2x−3) or (x+2), 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.
According to the Zero Product Property, for the entire function (2x−3)(x+2)=0 to equal 0, at least one of the factors, (2x−3) or (x+2), must equal 0. So, 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."
According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. In the given quadratic equation, (2x−3)(x+2)=0, the product of the factors is zero. Therefore, according to the Zero Product Property, at least one of the factors must be zero for the entire function to equal zero. Thus, 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.
