Practice Polynomials Over Rings - 19.2.9 | 19. Rings, Fields and Polynomials | Discrete Mathematics - Vol 3
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a polynomial of degree 2 over a ring.

💡 Hint: Consider the highest power term.

Question 2

Easy

What does closure property mean in the context of polynomials over a ring?

💡 Hint: Think about the operations performed.

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 degree of the polynomial P(x) = 5x^3 + 4x + 2?

  • 1
  • 2
  • 3

💡 Hint: Look at the power of x terms.

Question 2

True or False: The sum of two polynomials of degrees 2 and 3 will always yield a polynomial of degree 3.

  • True
  • False

💡 Hint: Think about which degree dominates.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Create two polynomials over a ring defined by integers modulo 4 and show their addition and multiplication. What is the result of each operation?

💡 Hint: Keep track of modulo operations throughout.

Question 2

Prove that the product of a polynomial of degree m and another of degree n has a degree of m+n.

💡 Hint: Visualize the polynomial terms’ expansion.

Challenge and get performance evaluation