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.
-$$6 x ^ { 3 } - 40 x ^ { 2 } + 54 x - 20 = 0 ; 1$$
A) $\left\{ \frac { 2 } { 3 } , 5,1 \right\}$
B) $\left\{ - \frac { 2 } { 3 } , 5,1 \right\}$
C) $\left\{ \frac { 2 } { 3 } , - 5,1 \right\}$
D) $\left\{ \frac { 5 } { 6 } , 4,1 \right\}$

Question

Quizplus · Accepted Answer

Using synthetic division with $x = 1$, the remainder is 0, confirming $x = 1$ is a solution. The reduced polynomial is $6x^2 - 34x + 20$, which factors to $(3x - 2)(2x - 10)$, giving solutions $x = \frac{2}{3}$ and $x = 5$.

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