Use the x-intercept method to find all real solutions of the equation x^3-6x^2+11x-6

I think that this is the x-intercept method:

First of all, we set y=x^3-6x^2+11x-6.

To find x, we need to let y=0. (y is also equals to f (x))

f (x) = x^3-6x^2+11x-6

In order to make f (x) = 0, what does x have to be?

f (1) = 0

So then we divide x^3-6x^2+11x-6 by x-1. Why? Because that will not give us a remainder.

(x^3-6x^2+11x-6) / (x-1) = x^2-5x+6

Now, we need to factorize it.

x^2-5x+6 = (x-2) (x-3)

So x=2,3