Question

question 12 select all z that satisfy the following equation: (4z(z + 1)(z + 2) = 0)
options: 0, 4, -1, 2, -2, 1 (with test instructions about time limit, multiple attempts, etc. above)

Explanation:

Step1: Recall Zero Product Property

The Zero Product Property states that if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \) (or both). For the equation \( 4z(z + 1)(z + 2)=0 \), we can set each factor equal to zero.

Step2: Solve for \( z \) from each factor

• For the factor \( 4z = 0 \):

Divide both sides by 4: \( z=\frac{0}{4}=0 \).

• For the factor \( z + 1 = 0 \):

Subtract 1 from both sides: \( z=-1 \).

• For the factor \( z + 2 = 0 \):

Subtract 2 from both sides: \( z=-2 \).
The factor 4 is a non - zero constant, so it does not contribute to the solution of the equation (since \( 4
eq0 \)).

Answer:

The values of \( z \) that satisfy the equation are \( 0 \), \( - 1 \), and \( -2 \). So the correct options are:

• \( 0 \)
• \( -1 \)
• \( -2 \)