Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$$

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x - 12$$

A) $- 3 ; f ( x ) = ( x + 3 ) \left( x ^ { 2 } - x - 4 \right)$
B) $- 3 , - 2,2 ; f ( x ) = ( x + 3 ) ( x + 2 ) ( x - 2 )$
C) $- 2 ; f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x - 6 \right)$
D) $- 2,2,3 ; f ( x ) = ( x + 2 ) ( x - 2 ) ( x - 3 )$