Answer
please see image:
Work Step by Step
End behavior:
When $ x\rightarrow-\infty$ , observing just the signs,
we have $-(-)(-)(-)$, so $ P(x)\rightarrow+\infty$
When $ x\rightarrow+\infty$ , observing just the signs,
we have $-(+)(+)(+)$, so $ P(x)\rightarrow-\infty$
Intercepts:
x-intercepts: $x=-2, x=0, x=3.$
y-intercept: $P(0)=0$
Short description of the graph, left to right:
- falls from the upper left,
- crosses the x-axis at x=-2,
- continues falling to a local minimum, turns and
- while rising, crosses the x-axis at the origin,
- continues rising to a local maximum, turns, and
- while falling, crosses the x-axis at x=3,
- continues falling indefinitely