Answer
(a) The graph is as shown.
(b) The $x$-intercepts are $(-1,0)$, $(0,0)$ and $(3,0)$.
(c) The solution is $x=-1,0,3$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
Work Step by Step
(a) The graph is as shown.
(b) The $x$-intercepts are $(-1,0)$, $(0,0)$ and $(3,0)$.
(c) Setting $y=0$:
$$0=x^3-2x^2-3x$$
$$x(x+1)(x-3)=0$$
$$x=0$$
$$x+1=0$$
$$x=-1$$
$$x-3=0$$
$$x=3$$
Thus, the solution is $x=-1,0,3$.
(d) The result in part (c) is the same with the $x$-intercepts of the graph.
