Use Division to Write the Rational Function in the Form $$\frac { x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x - 1 } { x ^ { 2 } - 4 x + 3 }$$

Multiple Choice

Use division to write the rational function in the form q(x) + r(x) /d(x) , where the degree of r(x) is less than the degree of
d(x) . Then find the partial fraction decomposition of r(x) /d(x) .
- $$\frac { x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 } - 3 x ^ { 2 } - 6 x - 1 } { x ^ { 2 } - 4 x + 3 }$$

A) $x ^ { 3 } + x ^ { 2 } - 2 x - 2 + \frac { - 19 } { 2 ( x - 3 ) } + \frac { - 11 } { 2 ( x - 1 ) }$
B) $x ^ { 3 } - x ^ { 2 } - 2 x + 2 + \frac { 19 } { 2 ( x - 3 ) } + \frac { - 11 } { 2 ( x - 1 ) }$
C) $x ^ { 3 } - x ^ { 2 } - 2 x - 2 + \frac { - 19 } { 2 ( x - 3 ) } + \frac { - 11 } { 2 ( x - 1 ) }$
D) $x ^ { 3 } + x ^ { 2 } + 2 x + 2 + \frac { - 19 } { 2 ( x - 3 ) } + \frac { 11 } { 2 ( x - 1 ) }$