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 )
Answer: The roots are: x 1= 3, x 2 = 4, x 3 = 7.
