Polynomial Inequality Homework: Solving without Technology | Remainder Theorem

In summary, the conversation is about solving a inequality without using technology and using the Remainder Theorem. The attempt at a solution involved setting the inequality equal to zero and checking for possible rational roots, but none worked. The person is looking for a different approach to solve the problem, as the current method is not working. The last comment mentions a possible error in the equation.
  • #1
Ethan_Tab
57
2

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

It seems it is only one single interval ?
 

1. What is a polynomial inequality?

A polynomial inequality is an inequality that involves a polynomial expression, which is an expression made up of variables and coefficients using the operations of addition, subtraction, and multiplication. It can also include exponents, but not division.

2. What is the Remainder Theorem?

The Remainder Theorem is a theorem in algebra that states that when a polynomial function is divided by a linear function of the form x - a, the remainder is equal to the value of the polynomial function at x = a. In other words, the remainder is the value left over after the polynomial is divided by (x - a).

3. Why is it important to know how to solve polynomial inequalities without technology?

Knowing how to solve polynomial inequalities without technology is important because it allows you to understand the underlying concepts and principles behind the solution process. It also helps in developing problem-solving skills and critical thinking abilities.

4. How do I solve a polynomial inequality without using technology?

To solve a polynomial inequality without technology, you can use a variety of methods such as graphing, factoring, and using the Remainder Theorem. You can also use algebraic manipulation to isolate the variable and solve for the inequality.

5. What are some common mistakes to avoid when solving polynomial inequalities?

Some common mistakes to avoid when solving polynomial inequalities include forgetting to switch the direction of the inequality when multiplying or dividing by a negative number, not checking for extraneous solutions, and making errors in algebraic manipulation. It is important to double-check your work and carefully follow the steps of the chosen method to avoid these mistakes.

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