# Irreducible Palindromic Polynomials, Reducible and Irreducible Polynomials and Degrees of Polynomials

Not what you're looking for?

3.- a) Determine the number of polynomials f(x) of degree 6 over for which f(1)=1 and f(0)=1.

b) Determine the number of polynomials of degree 6 over that are reducible but have no linear factors. How this is possible, please can you explain this?

Hint Consider the possible factorizations.

c) Determine the number of irreducible polynomials of degree 6 over . Explain.

In order to find this, is there a formula o we need to figure out by inspection?

4.- Show that there is an irreducible palindromic polynomial of degree 6 over .

Hint use problem #3

Please see the attached file for the fully formatted problems.

keywords: palindrome

##### Purchase this Solution

##### Solution Summary

Irreducible Palindromic Polynomials, Reducible and Irreducible Polynomials and Degrees of Polynomials are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

##### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Problem #3

(a) The polynomial with degree 6 over must have form

, where .

From the condition, we know

, ,

Thus we have , so there are odd number of 1's from to . There are possibilities.

Thus there are 16 polynomials with degree 6 over such that .

(b) Since has no linear factor, then . Because ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts