Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of $f ( x ) = 4 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1$ .

A) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real
B) 3 positive reals or 1 positive real; no negative reals
C) 0 positive real; 3 negative reals or 1 negative real
D) 1 positive real; 3 negative reals or 1 negative real
E) no positive reals; no negative reals