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

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, 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)
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

Answer 1

Based on the Zero Product Property, for the product of two factors to equal zero, at least one of the factors must equal zero. Therefore, the correct statement regarding the 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 indicates that to find the values of \(x\) where the equation holds true, you would set each factor equal to zero:

1. \(2x - 3 = 0\)
2. \(x + 2 = 0\)

From this, you can solve for \(x\) in both cases, leading to the solutions of the quadratic equation.