Answer:
f(x) = 
+ 2x³ - 4x² - 6x + 3
Step-by-step explanation:
Note that radical zeros occur in conjugate pairs, thus
- 1 + 
is a zero then - 1 - is also a zero
is a zero then - is also a zero
Thus the corresponding factors are
(x - (- 1 + ) ), (x - (- 1 - ) ), (x - ), (x - (- )), that is
(x + 1 - ), (x + 1 + ), (x - ), (x + )
The polynomial is then the product of the roots
f(x) = (x + 1 - )(x + 1 + )(x - )(x + )
= ((x + 1)² - ()²)((x² - ()²)
= (x² + 2x + 1 - 2)(x² - 3)
= (x² + 2x - 1)(x² - 3) ← distribute
= - 3x² + 2x³ - 6x - x² + 3
= + 2x³ - 4x² - 6x + 3
