Practice Existence of Irreducible Polynomials - 1.9 | Overview 41 | Discrete Mathematics - Vol 3
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Practice Questions

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Question 1

Easy

Define what a finite field is.

💡 Hint: Think about how many elements are included and what letters represent those elements.

Question 2

Easy

What defines an irreducible polynomial?

💡 Hint: Consider its ability to be broken down into simpler polynomials.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the characteristic of a finite field?

  • Any integer
  • An irrational number
  • A prime number

💡 Hint: Consider what properties of numbers define a field's characteristic.

Question 2

True or False: Every polynomial can be factored over finite fields.

  • True
  • False

💡 Hint: Think about polynomials that can and cannot be broken down further.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Prove that the polynomial x^2 + 1 is irreducible over GF(5).

💡 Hint: Evaluate the polynomial at each element of the field.

Question 2

Construct a field GF(2^3) using an irreducible polynomial.

💡 Hint: Identify coefficients for the polynomial from GF(2) and how they contribute to the field.

Challenge and get performance evaluation