Answer
(a) $x=5$ (multiplicity 3), $x=-4$ (multiplicity 2).
(b) crosses the x-axis at $x=5$, touches at $x=-4$.
(c) $4$.
(d) $y=x^5$.
Work Step by Step
(a) Given $f(x)=(x-5)^3(x+4)^2$, we can find zero(s) $x=5$ (multiplicity 3), $x=-4$ (multiplicity 2).
(b) The graph crosses the x-axis at $x=5$, touches at $x=-4$.
(c) The maximum number of turning points on the graph is $n-1=5-1=4$.
(d) The end behavior is similar to those of $y=x^5$.
