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] for which [tex]\( g(x) = 0 \)[/tex].
We start by setting the polynomial equal to zero:
[tex]\[ x^3 + 6x^2 - 9x - 54 = 0 \][/tex]
To solve this equation, we look for the roots of the polynomial. The roots (zeros) of a polynomial are the values of [tex]\( x \)[/tex] that satisfy the equation. Upon solving the equation, we find that the zeros are:
[tex]\[ x = -6, -3, 3 \][/tex]
These values are the solutions to the equation. Therefore, the zeros of the function [tex]\( g(x) = x^3 + 6x^2 - 9x - 54 \)[/tex] are:
[tex]\[ \boxed{-6, -3, 3} \][/tex]
Thus, the correct answer is:
B. [tex]\( 3, -3, -6 \)[/tex]
