Cubic non-linear inequality (HELP)

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The discussion centers on understanding a cubic non-linear inequality from a review test. Participants suggest plotting the cubic function and decomposing it to find zeros, which can help in analyzing the inequality across different intervals. It is noted that the function may have up to three zeros, and the direction of the inequality needs to be considered for each interval. The original poster struggles with identifying roots, mentioning that neither +1 nor -1 are roots, and the Rational Root Theorem is not applicable. Cardano's method is recommended as a potential solution for solving the cubic equation.
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I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
VlOaP.png
 
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I don't see any inequality.

As far as expressing the equation graphically, you just plot it.
 
aew782 said:
I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
VlOaP.png

Try to decompose the cubic expression to find the zeros, meaning find if possible its linear and any quadratic factors (if quadratic factor cannot be factored further). It may have as many as three zeros, but not more. The function (now being equal to zero) is in possibly four intervals. You don't show us the direction of your inequality but you say you want to analyze the inequality; but anyway, you check the quality of the value of the "inequality" for each interval of the x-axis and determine if the x value is true for the inequality or false.

EDIT: harder than I thought. +1 is not a root and -1 is not a root. Rational Root theorem will not work.
 
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