Write the Function in the Form F(x) = (X - $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Multiple Choice

Write the function in the form f(x) = (x - k) q(x) + r for the given value of k and demonstrate that f(k) = r. $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

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