Find a Fifth Degree Polynomial Function of the Lowest Degree $- 4 , - 1,0,1,4$

Multiple Choice

Find a fifth degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one. $- 4 , - 1,0,1,4$

A) $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } + 27 x ^ { 2 } + 36 x$
B) $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } - 13 x ^ { 3 } - 27 x ^ { 2 } + 36 x$
C) $f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - 19 x ^ { 3 } - 16 x ^ { 2 } + 48 x$
D) $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } - 13 x ^ { 3 } - x ^ { 2 } + 12 x$
E) $f ( x ) = x ^ { 5 } - 17 x ^ { 3 } + 16 x$