Use the Zero Product Property to find the value of x that makes the following statement true: 2⋅(x−3)=0

Question

.(1 point)
The value that makes the statement true is x=
.

Answer 1

To use the Zero Product Property, we start with the equation:

\[ 2 \cdot (x - 3) = 0. \]

According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must be zero. Here, we have:

1. The factor \(2\), which cannot be equal to zero since it's a non-zero constant.
2. The factor \((x - 3)\).

Since \(2\) is not equal to zero, we set the other factor equal to zero:

\[ (x - 3) = 0. \]

Now, solve for \(x\):

\[ x - 3 = 0 \] \[ x = 3. \]

Thus, the value that makes the statement true is:

\[ x = 3. \]

Answer 2

Zavier, Boaz, and Sophie are trying to find the values of x that make the following quadratic function equal 0: x(x+2)=0
. Each student came up with a different answer, which they explained in the options. Which student’s explanation is correct?

Option #1: Zavier says that only x=−2
will make the function equal 0, and he provided the given work: −2⋅(−2+2)=−2⋅(0)=0
.

Option #2: Boaz says that the values x=0
and x=−2
will both make the function equal 0, and he provided the given work: 0⋅(0+2)=0⋅(2)=0
, and −2⋅(−2+2)=−2(0)=0
.

Option #3: Sophie says that only x=0
will make the function equal 0, and she provided the given work: 0⋅(0+2)=0⋅(2)=0
.

(1 point)
Option #
is the correct explanation.