Divide using synthetic division, and write a summary statement in fraction form.
-$$\frac { 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x } { x + 3 }$$
A) $2 x ^ { 3 } + 5 x ^ { 2 } + 3 + \frac { 9 } { x + 3 }$
B) $2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 + \frac { - 45 } { x + 3 }$
C) $2 x ^ { 3 } - 5 x ^ { 2 } + 3 + \frac { - 9 } { x + 3 }$
D) $2 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 15 + \frac { 45 } { x + 3 }$

Question

Quizplus · Accepted Answer

The synthetic division of $2x^4 - x^3 - 15x^2 + 3x$ by $x + 3$ results in $2x^3 - 7x^2 + 6x - 15$ with a remainder of 45, giving the fraction form $\frac{45}{x+3}$.

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