Write $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 13 x + 22$

Multiple Choice

Write $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + 13 x + 22$ in the form $f ( x ) = ( x - k ) q ( x ) + r$ when k = -5.

A) $f ( x ) = ( x + 5 ) \left( x ^ { 2 } + 2 x + 3 \right) + 7$
B) $f ( x ) = ( x + 5 ) \left( x ^ { 2 } - 2 x + 3 \right) - 7$
C) $f ( x ) = ( x - 5 ) \left( x ^ { 2 } + 2 x + 3 \right) - 7$
D) $f ( x ) = ( x - 5 ) \left( x ^ { 2 } - 2 x + 3 \right) + 7$
E) $f ( x ) = ( x + 5 ) \left( x ^ { 2 } + 2 x + 3 \right)$