Solve the Polynomial Equation $$x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0$$

Multiple Choice

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
- $$x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0$$

A) $\{ 1,2 + \sqrt { 2 } , 2 - \sqrt { 2 } \}$
B) $\{ 1 , - 1,2 \}$
C) $\{ - 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$
D) $\{ 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$