Answer
$P(x)=x^{3}(x+3)(x-3)$
Zeros: 0,+3,-3
Graph: See image below.
Work Step by Step
Factor out $x^{3}$
P(x) = $x^{3}(x^{2}-9)$. The second term is a perfect square. (+3 and -3 are factors of 9 whose sum is 0).
$P(x)=x^{3}(x+3)(x-3)$
Zeros: 0,+3,-3
The degree of the polynomial is 5. The leading coefficient is positive. The end behavior of $x^{5}$ is positive infinity for $x\gt0$ and negative infinity for $x\lt0$. There are zeros at 0,3 and -3. The graph represents $-x^{3}$ in the middle of the two intercepts. The graph starts from negative infinity and It has a local max at x=-2.324 where the y-value is 45.174 and a local min at x=+2.324 and y=-45.174 where the graph reverses direction and shoots up.
