Find the roots of f(x) = x3 − 14x2 + 61x − 84?

F ( 3 ) = 27 - 126 + 183 - 94
Therefore, f ( x ) is divisible by ( x - 3 ):
( x³ - 14 x² + 61 x - 84 ) : ( x - 3 ) = x² - 11 x + 28
-x³  + 3 x²

      - 11 x² + 61 x
      + 11 x² - 33 x
       
                    28 x - 84
                   - 28 x + 84
                   
                     R ( x ) = 0
After that:
x² - 11 x + 28 = x² - 7 x - 4 x + 28 = x ( x - 7 ) - 4 ( x - 7 ) = 
= ( x - 7 ) ( x - 4 )
The roots are: x 1= 3,  x 2 = 4,  x 3 = 7.

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