Step-by-step explanation:
[tex]f(x) = x^3 - 3x^2 - 4x[/tex]
factor it: (start by factoring out the x that is common to all 3 )
[tex]= x\left(x^2-3x-4\right)[/tex]
next keep factoring the inside...
[tex]= x\left(x^2+x-4x-4\right)\\=x \left[x\left(x+1\right)-4\left(x+1\right)\right]\\=\bold{x\left(x+1\right)\left(x-4\right)}[/tex]
So, the only way the function [tex]f(x)[/tex] can be [tex]0[/tex] is if:
C. [tex]\{-1,0,4\}[/tex]
