Question 251202
We can factor x^3-3x+2<=0 into

(X+2)(X-1)^2 <= 0

Now we would look at where X+2 is +, 0, and -. 
We see that it is negative for all x < -2, zero at x = -2, positive at X > -2.

Now we would look at where(X-1)^2 is +, 0, and -. 
We know that any number squared can = 0 or be positive. We see that the answer is zero if x = 1, and positive every where else. 

We want answers that are either zero or negative. This occurs on the interval X <=-2.