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