Polynomial Inequality Homework: Solving without Technology | Remainder Theorem

[Ethan_Tab]

Homework Statement

solve 3x⁴+2x²-4x+6≥6x⁴-5x³-9x+2

Do not use technology (i.e.-graphing calculators)

Homework Equations

Remainder Theorem

The Attempt at a Solution

I set the inequality equal to zero
-3x⁴+5x³+3x²+5x+4≥0

Checking all the Possible rational roots for a possible factors... none worked... therefore roots not nice numbers. I was hoping to get this factored down and do an interval test and go about it from there but that won't work. Is there a different way to approach this question?

 

[davidmoore63@y]

Looks like it should be 2x^2 not 3x^2

 

[jk22]

If you look at -3x^4+2x^2+4>-5x^3-5x

It seems it is only one single interval ?