SOLUTION: Find the solution to the polynomial inequality x^3+5x^2-4x-20>0 thanks:)

Question 968367: Find the solution to the polynomial inequality x^3+5x^2-4x-20>0
thanks:)
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Roots are -5, -2, 2. That much you would find using Rational Roots Theorem and synthetic division.

You can test the intervals, but you could also make use of characteristic knowledge of how the shapes of cubic functions are. Cubic, degree 3; two humps; function rises from the far left and rises to the far right. You KNOW the inequality is false to the left of -5, and you KNOW the inequality is true to the right of 2.

Figure on the rest.

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Unsure of the inequality but found roots on your own:

Test a value inside each interval. Which intervals have values which satisfy the inequality, and which intervals do not satisfy the inequality?

The roots found cut the x-axis into specific intervals:

-
Literally pick a value in each interval and test to see if it makes the inequality true.

Another tutor showed the final answer. That answer is correct.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the solution to the polynomial inequality x^3+5x^2-4x-20>0
***
use rational roots theorem with synthetic division
...0...|.....1......5......-4......-20......
...1...|.....1......6.......2......-18.
...2...|.....1......7......10.......0 (2 is a root)
f(x)=(x-2)(x^2+7x+10)=(x-2)(x+5)(x+2)>0
number line:
<....-....-5.....+.....-2.....-.....2.....+......>
solution: (-5, -2) U (2, ∞)
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