To find the zeros of the polynomial function [tex]\( g(x) = x^3 + 6x^2 - 9x - 54 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] such that [tex]\( g(x) = 0 \)[/tex].
Let's follow a step-by-step approach to solving this polynomial equation:
1. Identify the polynomial equation:
The given polynomial equation is:
[tex]\[
g(x) = x^3 + 6x^2 - 9x - 54
\][/tex]
2. Set the polynomial equal to zero:
We need to solve for [tex]\( x \)[/tex] in the equation:
[tex]\[
x^3 + 6x^2 - 9x - 54 = 0
\][/tex]
3. Determine the zeros of the polynomial:
The zeros of a polynomial are the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( g(x) = 0 \)[/tex].
Through our calculations, we find that the zeros of the polynomial [tex]\( g(x) \)[/tex] are:
[tex]\[
x = -6, -3, 3
\][/tex]
4. Select the correct answer based on the found zeros:
Given the options, the correct answer that includes [tex]\( -6, -3, 3 \)[/tex] is:
[tex]\[
\text{B. } -6, -3, 3
\][/tex]
Therefore, the correct answer to the question "What are the zeros of [tex]\( g(x) = x^3 + 6x^2 - 9x - 54 \)[/tex]?" is:
[tex]\[
\text{B. } -6, -3, 3
\][/tex]
