Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

A) $x = 0$ , multiplicity $2 ; x = - 2$ , multiplicity $1 ; x = - 6$ , multiplicity 1
B) $x = 2$ , multiplicity $2 ; x = 6$ , multiplicity 2
C) $x = 0$ , multiplicity $2 ; x = 2$ , multiplicity $1 ; x = 6$ , multiplicity 1
D) $x = - 2$ , multiplicity $2 ; x = - 6$ , multiplicity 2
E) $x = 0$ , multiplicity $1 ; x = 2$ , multiplicity $1 ; x = - 2$ , multiplicity $1 ; x = 6$ , multiplicity 1