Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$$

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.
- $$f ( x ) = 2 x ^ { 4 } - 12 x ^ { 3 } + 19 x ^ { 2 } - 6 x + 9$$

A) $- 3,3 ; f ( x ) = ( x - 3 ) ( x + 3 ) \left( 2 x ^ { 2 } + 1 \right)$
B) no real roots; $f ( x ) = \left( x ^ { 2 } + 9 \right) \left( 2 x ^ { 2 } + 1 \right)$
C) 3 , multiplicity $2 ; f ( x ) = ( x - 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$
D) $- 3$ , multiplicity $2 ; f ( x ) = ( x + 3 ) ^ { 2 } \left( 2 x ^ { 2 } + 1 \right)$