Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

A) $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$
B) $x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1$
C) $x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1$
D) $x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2$
E) $x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1$