x^3 - 6x^2 + 11x - 6 = 0
f(1) = 1^3 - 6(1)^2 + 11(1) - 6 = 1 - 6 + 11 - 6 = 0
This means that x - 1 is a factor of x^3 - 6x^2 + 11x - 6 = 0
x^2 - 5x + 6
___________________
x - 1 | x^3 - 6x^2 + 11x - 6
- | x^3 - x^2
|______________
| -5x^2 + 11x - 6
- | -5x^2 + 5x
|_____________________
| 6x - 6
- | 6x - 6
x^3 - 6x^2 + 11x - 6 = (x - 1)(x^2 - 5x + 6) = (x - 1)(x - 2)(x - 3)
Therefore, solutions to x^3 - 6x^2 + 11x - 6 are 1, 2 and 3.
