solving inequalities: x^3 > 3x - 2

[whiteti]

x³ > 3x-2

so i moved everything over to one side

x³-3x+2>0

I'm pretty sure I cant factor because of the x³
Do I guess and check for a root which will lead to long division?

Thanks

 

[DrPhil]

x³ > 3x-2

so i moved everything over to one side

x³-3x+2 > 0

I'm pretty sure I cant factor because of the x³
Do I guess and check for a root which will lead to long division?

Thanks

The only possible rational roots would be x=1 or x=2. Have you tried those as possible roots?

If you do find a root and then divide it out, you will have an irreducible quadratic as a factor. Such a factor never changes sign (since it has no roots), so you will be able to find where the inequality is true.

 

[lookagain]

The only possible rational roots would be x=1 or x=2. Have you tried those as possible roots?

The only possible rational roots would actually be \(\displaystyle \ x = \pm 1 \ \ or \ \ x = \pm 2 \ \ \) due to the Rational Root Theorem.