Question 1151023
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A shorthand way of saying "(x+1)(x-2) is positive" is to write (x+1)(x-2) > 0


Change the inequality sign to an equal sign. Then solve for x using the zero product property.


(x+1)(x-2) = 0
x+1 = 0 or x-2 = 0
x = -1 or x = 2


If x = -1 or x = 2, then (x+1)(x-2) is equal to zero.


Draw a number line. Plot -1 and 2 on the number line. This drawing is optional, but it might help you see the three distinct regions.
<img src = "https://i.imgur.com/mNaUkU6.png">

Region A in red represents everything to the left of -1. 
Let's pick one value from this region, say x = -2
(x+1)(x-2) > 0
(-2+1)(-2-2) > 0 ... plug in x = -2
(-1)(-4) > 0
4 > 0
The last inequality is true, so any value less than -1 will make (x+1)(x-2) > 0 true.


Move onto region B in blue. This is the set of numbers between -1 and 2. Pick something from this region, say  x = 0, and plug it in to get
(x+1)(x-2) > 0
(0+1)(0-2) > 0
(1)(-2) > 0
-2 > 0
The last inequality is false, so any value between -1 and 2 will make (x+1)(x-2) > 0 false.


Finally let's check region C in green. Pick a value to the right of 2. I'll pick x = 3.
(x+1)(x-2) > 0
(3+1)(3-2) > 0
(4)(1) > 0
4 > 0
The last inequality is true, so any value larger than 2 will make (x+1)(x-2) > 0 true.


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So,
<ul><li>if x < -1, then (x+1)(x-2) > 0 is true.</li><li>if -1 < x < 2, then (x+1)(x-2) > 0 is false.</li><li>if x > 2, then (x+1)(x-2) > 0 is true.</li></ul>


This is why the final answer is A. x < -1 or x > 2
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