Find All of the Real Zeros of the Function $$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 17 x ^ { 2 } - 4 x + 30$$

Multiple Choice

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- $$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 17 x ^ { 2 } - 4 x + 30$$

A) $- 5$ (rational) , 3 (rational) , $2 + \sqrt { 2 }$ (irrational) , and $2 - \sqrt { 2 }$ (irrational)
B) 5 (rational) , $- 3$ (rational) , $\sqrt { 2 }$ (irrational) , and $- \sqrt { 2 }$ (irrational)
C) $- 5$ (rational) , 3 (rational) , $\sqrt { 2 }$ (irrational) , and $- \sqrt { 2 }$ (irrational)
D) 5 (rational) , $- 3$ (rational) , $2 + \sqrt { 2 }$ (irrational) , and $2 - \sqrt { 2 }$ (irrational)