SOLUTION: Solve {{{x^3+2x^2-11x-12<0}}}
Algebra.Com
Question 135536: Solve
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Set the left side equal to zero.
When we use a graphing calculator, we find that the solutions are , and . So that means that the inequality factors to
Now plot the critical values on a number line
So let's evaluate a point that is to the left of 
(which is the left most endpoint). Let's evaluate the value
(x+1)(x-3)<0)
Start with the given inequality
(-5+1)(-5-3)<0)
Plug in
Evaluate and simplify
Since is true, this means that one part of the solution in interval notation is )
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Now let's test a point that is in between the critical values and 
Start with the given inequality
(-2+1)(-2-3)<0)
Plug in
Evaluate and simplify
Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
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Now let's test a point that is in between the critical values and 
Start with the given inequality
(1+1)(1-3)<0)
Plug in
Evaluate and simplify
Since is true, this means that one part of the solution in interval notation is )
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So let's evaluate a point that is to the right of (which is the right most endpoint). Let's evaluate the value
Start with the given inequality
(4+1)(4-3)<0)
Plug in
Evaluate and simplify
Since is false, this means that the interval does not work. So that means that this interval is not in the solution set and can be ignored.
-----------------------------------------------
Answer:
So the solution set in interval notation is \cup\left(-1,3\right))
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