Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }$$
A) $x ^ { 2 } + 3 x + 4$
B) $x ^ { 2 } + 3 x + 2$
C) $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 2 } { x + 1 }$
D) $x ^ { 2 } + \frac { 13 } { 3 } x + \frac { 14 } { 9 } + \frac { 16 } { 27 }$

Question

Quizplus · Accepted Answer

To perform synthetic division with $\frac{1}{3}$, we set up the coefficients: $1, \frac{8}{3}, 1, -\frac{2}{3}$. Bringing down the first coefficient (1), multiplying it by $\frac{1}{3}$ gives $\frac{1}{3}$, which is added to the second coefficient to get $3$. Repeating this process, $3 \times \frac{1}{3} = 1$, added to the third coefficient gives $2$. Finally, $2 \times \frac{1}{3} = \frac{2}{3}$, added to the last coefficient gives $0$, indicating no remainder. The result is $x^2 + 3x + 2$.

Use Synthetic Division to Perform the Division x3+83x2+1x−23x−13\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }x−31​x3+38​x2+1x−32​​

Use Synthetic Division to Perform the Division $\frac { x ^ { 3 } + \frac { 8 } { 3 } x ^ { 2 } + 1 x - \frac { 2 } { 3 } } { x - \frac { 1 } { 3 } }$