Answer
(a) $x=3$ (multiplicity 1).
(b) $x=3$ crosses the x-axis.
(c) $6$.
(d) $y=2x^7$.
Work Step by Step
(a) For $f(x)=2(x-3)(x^2+4)^3$, we can list real zero as $x=3$ (multiplicity 1).
(b) At $x=3$ the graph crosses the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=7-1=6$.
(d) As $n=7, a_7\gt0$, the end behaviors are rise to the right and fall to the left similar to $y=2x^7$.
