Indicate the set of all $x$ satisfying the following conditions $(x+1)(x-1)(x-2) > 0$ Solution check Indicate the  set of all $x$ satisfying the following conditions: $$(x+1)(x-1)(x-2) > 0$$
One of the sets is $$(2, \infty)$$
I'm more concerned about obtaining the second set. A solution says $$(-1,1)$$, but I don't see how that is possible unless there was a typo in the text and the author meant $$(1-x)(x-1)(x-2) > 0$$ as the question.
 A: You want a product of three real numbers to be positive.  That only occurs if all three are positive or two terms are negative the third is positive.  (One negative, or all three negative result in the product being negative.)
$x - 2 < x - 1 < x + 1$ so all are positive when $x+ 1> x - 1 > x - 2 > 0 \iff x > 2$ so $(2, \infty)$ is one interval.
To get one term positive and two negative you need $x + 1 > 0 > x-1 > x-2$>  In other words $x+1 > 0$ and $x -1 < 0$ or in other words $x > -1$ and $x < 1$.  So $(-1,1)$ is the other interval.
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or another way to think of it:
There are three spots, $x - 2 = 0$, $x -1 = 0$, and $x + 1 = 0$ where the signs of the terms change polarity.  So we only need to consider the intervals: $(-\infty, -1),(-1,1),(1,2)$ and $(2, \infty)$.  By direct application we can see two result in negative products and two in positive.
A: $(-1, 1)$ is indeed the second set. 
When $-1<x<1$, the first factor $(x+1)$ will be positive and the next two factors will be negative. A positive number multiplied by two negatives nets a positive number, thus an x in this range will produce a positive product.
A: $(x+1)(x-1)(x-2) = 0$ when $x \in \{-1,1,2\}$
When $x<-1,$$\\
(x+1)<0\\
(x-1)<0\\
(x-2)<0$
Negative* negative * negative  is negative.
When $-1<x<1,$$\\
(x+1)>0\\
(x-1)<0\\
(x-2)<0$
positive * negative * negative  is positive.
etc.
A: Building a plot can help you a lot.

