Which of the following represents the zeros of the function

g (x) = x3 - 9x2 + 2x + 48?

A. x = - 8, x = 2, and x = - 3

B. x = 8, x = - 2, and x = 3

C. x = 6, x = - 4, and x = 9

D. x = - 6, x = 4, and x = - 9

g (x) = x^3 - 9x^2 + 2x + 48?

Probe some roots. When you use x = - 2

you will have: (-2) ^3 - 9 (-2) ^2 + 2 (-2) + 48 = - 8 - 36 - 4 + 48 = 0

So, - 2 is a root

From that you can divide x^3 - 9x^2 + 2x + 48 by x + 2 and you will get

x^2 - 11x + 24

Then you can factor that: (x - 8) (x - 3)

So, the three roots are x = - 2, x = 3 and x = 8, which is the option B.

Answer: option B. x = 8, x = - 2, and x = 3