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

Using synthetic division with 3, the remainder is 0, confirming 3 is a root. The quotient is $3x^2 + x - 10$, which factors to $(3x - 5)(x + 2)$, giving 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