Answer
(a) $x=2$ (multiplicity 3).
(b) $x=2$ crosses the x-axis.
(c) $4$.
(d) $y=4x^5$.
Work Step by Step
(a) For $f(x)=4(x^2+1)(x-2)^3$, we can list real zero as $x=2$ (multiplicity 3).
(b) At $x=2$ the graph crosses the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=5-1=4$.
(d) As $n=5, a_5\gt0$, the end behaviors are rise to the right and fall to the left similar to $y=4x^5$.
