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)

Question

Responses

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.

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.

Answer 1

Based on the Zero Product Property, the correct statement about the quadratic equation \((2x−3)(x+2)=0\) 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 if the product of two factors equals zero, at least one of the factors must be equal to zero.