Divide using synthetic division, and write a summary statement in fraction form.
-$\frac { 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 } { x + 2 }$
A) $3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 + \frac { - 13 } { x + 2 }$
B) $3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 + \frac { - 25 } { x + 2 }$
C) $3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x + \frac { - 15 } { x + 2 }$
D) $3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 + \frac { 23 } { x + 2 }$

Question

Quizplus · Accepted Answer

The correct result of the synthetic division is $3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12$ with a remainder of $-25$, which is expressed as $\frac{-25}{x+2}$.

Divide Using Synthetic Division, and Write a Summary Statement in Fraction