Answer
$0,1,$ and $-1$
Work Step by Step
The given function is
$\Rightarrow h(x)=x(x^2-1)$
Substitute $0$ for $h(x)$.
$\Rightarrow 0=x(x^2-1)$
$\Rightarrow 0=x(x^2-1^2)$
Use difference of two squares pattern.
$\Rightarrow 0=x(x-1)(x+1)$
Use zero product property.
$\Rightarrow x=0$ or $x-1=0$ or $x+1=0$
Solve for $x$.
$\Rightarrow x=0$ or $x=1$ or $x=-1$
Hence, the zeros of the function are $0,1,$ and $-1$.
