Polynomial Inequality Homework: Solving without Technology | Remainder Theorem

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SUMMARY

The discussion focuses on solving the polynomial inequality 3x4 + 2x2 - 4x + 6 ≥ 6x4 - 5x3 - 9x + 2 without the use of technology. The Remainder Theorem is referenced as a potential tool, but the user struggles to find rational roots for factoring. The conclusion indicates that the polynomial may only have one interval of interest, suggesting a need for alternative analytical methods to solve the inequality.

PREREQUISITES
  • Understanding of polynomial inequalities
  • Familiarity with the Remainder Theorem
  • Knowledge of rational root theorem
  • Ability to perform interval testing
NEXT STEPS
  • Study the application of the Remainder Theorem in polynomial division
  • Learn about synthetic division for polynomial factorization
  • Explore methods for analyzing polynomial behavior without technology
  • Research interval testing techniques for polynomial inequalities
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Students tackling polynomial inequalities, educators teaching algebra concepts, and anyone interested in mastering manual methods for polynomial analysis.

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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?
 
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Looks like it should be 2x^2 not 3x^2
 
If you look at -3x^4+2x^2+4>-5x^3-5x

It seems it is only one single interval ?
 

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