Write the Equation of a Polynomial Function with the Given $x$

Multiple Choice

Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make
the degree of the function as small as possible.
-Crosses the $x$ -axis at $- 2,0$ , and 4 ; lies below the $x$ -axis between $- 2$ and 0 ; lies above the $x$ -axis between 0 and 4 .

A) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 8 x$
B) $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 8 x$
C) $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 } + 8 x$
D) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 8 x$