Use Multiplication or Division of Power Series to Find the First

Multiple Choice

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function. $$f ( x ) = 5 e ^ { - x ^ { 2 } } \cos 4 x$$

A) $5 \left( 1 - 17 x ^ { 2 } + \frac { 115 } { 6 } x ^ { 4 } \right)$
B) $5 \left( 1 - 9 x ^ { 2 } + \frac { 115 } { 6 } x ^ { 4 } \right)$
C) $5 \left( 1 - 9 x + \frac { 115 } { 6 } x ^ { 4 } \right)$
D) $5 \left( 1 - 9 x ^ { 2 } + \frac { 97 } { 6 } x ^ { 4 } \right)$
E) $5 \left( 1 - 17 x ^ { 2 } + \frac { 67 } { 6 } x ^ { 4 } \right)$