Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
-$$3 x ^ { 3 } + 8 x ^ { 2 } - 13 x - 30 = 0 ; - 3$$
A) $\left\{ - \frac { 5 } { 3 } , 2 , - 3 \right\}$
B) $\left\{ \frac { 5 } { 3 } , 2 , - 3 \right\}$
C) $\left\{ - \frac { 5 } { 3 } , - 2 , - 3 \right\}$
D) $\left\{ \frac { 2 } { 3 } , - 5 , - 3 \right\}$

Question

Quizplus · Accepted Answer

Synthetic division confirms -3 is a root, leaving a quotient of $3x^2 - x - 10$. Solving $3x^2 - x - 10 = 0$ gives roots $-\frac{5}{3}$ and $2$. Thus, the solutions are $\left\{ - \frac { 5 } { 3 } , 2 , - 3 \right\}$.

Use Synthetic Division to Show That the Number Given to the Right