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

Question

(
2
𝑥
−
3
)
(
𝑥
+
2
)
=
0
?(1 point)
Responses

Neither of the factors, (2x−3)
(
2
𝑥
−
3
)
nor ​(x+2)
​
(
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.

Both factors, (2x−3)
(
2
𝑥
−
3
)
and ​(x+2)
​
(
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.

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

Answer 1

The correct response based on the Zero Product Property 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 Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be equal to zero. Therefore, for the equation \((2x−3)(x+2)=0\) to hold true, either \(2x−3=0\) or \(x+2=0\) must be true.