Question

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

Explanation:

Step1: Set f(x) to zero

To find the zeros of the function \( f(x) = (x - 3)(x + 7)(x + 3) \), we start by setting \( f(x) = 0 \). So we have the equation:

$$ (x - 3)(x + 7)(x + 3) = 0 $$

Step2: Apply the zero - product property

The zero - product property states that if \( a\times b\times c = 0 \), then at least one of \( a = 0 \), \( b = 0 \), or \( c = 0 \) must be true.

• 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: \( x=-7 \).

• For the factor \( x + 3 \):

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

Answer:

3, -7, -3