Graph the polynomial \(P(x)=(x+1)^2(2-x)^3\) on the grid below, clearly identifying all axis intercepts. (3 marks)
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\(P(x)=(x+1)^2(2-x)^3 \ \ \Rightarrow\ \ \text{zeros at} \ \ x=-1,2\)
\(\text{At} \ \ x=-1, m (\text{multiplicity})=2 \ \ \Rightarrow\ \ \text{curve is a tangent to} \ x \text{-axis}\)
\(\text{At} \ \ x=2, m=3 \ \ \Rightarrow\ \ \text{curve has horizontal POI.}\)
\(\text{At} \ \ x=0, P(x)=(1)^2(2)^3=8\)