Use Synthetic Division to Divide F(x)by X - C, and Then

Multiple Choice

Use synthetic division to divide f(x) by x - c, and then write f(x) in the form f(x) = (x - c) q(x) + r.
- $$f ( x ) = x ^ { 5 } - 3 x ^ { 4 } - 7 x ^ { 3 } - 12 x ^ { 2 } - 13 x - 7 ; x - 5$$

A) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2 \right) + 3$
B) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x + 3 \right) + 0$
C) $( x - 5 ) \left( x ^ { 3 } + 2 x ^ { 2 } + 3 x + 3 \right) + 3$
D) $( x - 5 ) \left( x ^ { 4 } + 2 x ^ { 3 } + 3 x ^ { 2 } + 3 x - 2 \right) + 5$