Answer: \(p(x)=3(x+2)(x+1)(x-4)\) or \(p(x)=-3(x+2)(x+1)(x-4)\).

The graph crosses the \(x\)-axis at

\(x=-2,\quad x=-1,\quad x=4.\)

So the cubic must have the form

\(p(x)=k(x+2)(x+1)(x-4).\)

From the diagram, the curve crosses the \(y\)-axis at \(24\) or \(-24\), depending on which of the two possible orientations is used. When \(x=0\),

\((x+2)(x+1)(x-4)=2\cdot1\cdot(-4)=-8.\)

Hence \(-8k=24\) gives \(k=-3\), and \(-8k=-24\) gives \(k=3\).

Therefore the two possible expressions are

\(p(x)=3(x+2)(x+1)(x-4)\)

or

\(p(x)=-3(x+2)(x+1)(x-4).\)