Answer:
[tex](x-1)(x-(\frac{-1-i\sqrt{3}}{2}))(x+(\frac{-1+i\sqrt{3}}{2}))[/tex]
Step-by-step explanation:
Given equation : [tex]f(x)=x^3-1[/tex]
To write it's factored form :
⇒ [tex]x^3-1=0[/tex]
⇒[tex](x-1)(x^2+x+1)[/tex]
⇒[tex](x-1)(x-(\frac{-1-i\sqrt{3}}{2}))(x+(\frac{-1+i\sqrt{3}}{2}))[/tex]
⇒[tex] x=1,x=\frac{-1-i\sqrt{3}}{2}),x=\frac{-1+i\sqrt{3}}{2}[/tex]
⇒[tex] x=1,\frac{-1-i\sqrt{3}}{2},\frac{-1+i\sqrt{3}}{2}[/tex]
