Practice Irreducible Polynomials - 20.5 | 20. Polynomials Over Fields and Properties | Discrete Mathematics - Vol 3
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Irreducible Polynomials

20.5 - Irreducible Polynomials

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the definition of an irreducible polynomial?

💡 Hint: Think about polynomials contributing to factorization.

Question 2 Easy

Identify whether (x² + 3) is irreducible in real numbers.

💡 Hint: Consider possible factor pairs.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is an irreducible polynomial?

A polynomial that can be factored
A non-constant polynomial with no non-constant factors
A polynomial that can be divided by constant only

💡 Hint: Focus on the definition of irreducibility.

Question 2

True or False: All polynomials are reducible.

True
False

💡 Hint: Recall examples of irreducible polynomials.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Determine the irreducibility of the polynomial p(x) = x³ + x² + 1 in Z₂ and justify your answer.

💡 Hint: Test it against available values in Z₂.

Challenge 2 Hard

Given q(x) = x⁴ + 2x² + 1, prove it is reducible in Z₄.

💡 Hint: Factor it step-by-step.

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