Question

find the zeros of the function g(x).
g(x) = (x + 1)(x - 3)(x + 7)
write your answer as a list of values separated by commas.
x =

Explanation:

Step1: Set g(x) to zero

To find the zeros of the function \( g(x) \), we set \( g(x) = 0 \). So we have the equation:
\( (x + 1)(x - 3)(x + 7) = 0 \)

Step2: Apply the zero - product property

The zero - product property states that if \( a\times b\times c=0 \), then either \( a = 0 \), or \( b = 0 \), or \( c = 0 \).

• For the factor \( x + 1 \):

Set \( x+1=0 \). Solving for \( x \), we subtract 1 from both sides of the equation: \( x=- 1 \).

• For the factor \( x - 3 \):

Set \( x - 3=0 \). Solving for \( x \), we add 3 to both sides of the equation: \( x = 3 \).

• For the factor \( x + 7 \):

Set \( x+7=0 \). Solving for \( x \), we subtract 7 from both sides of the equation: \( x=-7 \).

Answer:

-1, 3, -7