how do i figure this out

what represennts the zeros of the function g(x)= x 3 - 9x 2+ 2x + 48

x^{3}-9x^{2}+2x+48

Put x= -2

-8-9*4+2*(-2)+48= -8-36-4+48=0

Hence (x+2) is a factor of x^{3}-9x^{2}+2x+48

(x^{3}-9x^{2}+2x+48) = (x+2)(x^{2}-11x+24)= (x+2)(x^{2}-8x-3x+24)=(x+2)[x(x-8)-3(x-8)]

=(x+2)(x-3)(x-8)

Hence (x+2)(x-3)(x-8)=0

x+2=0 or x-3 =0 or x-8 =0

x=-2 or x =3 or x =8

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