hello there welcome to study pool

to find the zeros we should factor the equation

we can factor as fallows

g(x)=x^3-8/x^2+1

we can write 8 as 2^3

then

g(x)=x^3-2^3/x^2+1

=(x-2)(x^2+2x+4)/x^2+1

let g(x)=0 to find zero values

(x-2)(x^2+2x+4)=0

x-2=0 or x^2+2x+4=0

x=2 or (x+1)^2-1+4=0

x=2 or (x+1)^2=-3

x=2 or (x+1)=(-3)^1/2

x=2 or x=-1+(3i)^1/2 or x=-1-(3i)^1/2

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