What Do You Know About Absolutely Irreducible Polynomials?

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What Do You Know About Absolutely Irreducible Polynomials?

For one, the title is self explanatory; this quiz assess your knowledge of absolutely irreducible polynomials. In the field of mathematics, these are polynomials that are irreducible or indivisible over a complex numbe, the complex field, or every algebraic extension of their respective selves. In general, they are multivariate polynomials defined over the rational numbers.


Questions and Answers
  • 1. 
    For a rational number to be absolutely irreducible, what field must it pass through? 
    • A. 

      Simple field

    • B. 

      Complex field

    • C. 

      Compound field

    • D. 

      Multiple field

  • 2. 
    For field K, how do we describe if the field is irreducible? 
    • A. 

      Algebraic extension of K

    • B. 

      Geometric extension of K

    • C. 

      Trigonometry rate of K

    • D. 

      Multiple patterns of K

  • 3. 
    What is the synonym of an absolutely irreducible algebraic set? 
    • A. 

      Algebraic variety

    • B. 

      Geometric variety

    • C. 

      Algebraic expression

    • D. 

      Geometric expression

  • 4. 
    Which algebraic group is the absolutely irreducible applied to? 
    • A. 

      Geometric representation

    • B. 

      Algebraic representation

    • C. 

      Linear representation

    • D. 

      Random representation

  • 5. 
    How do we represent the absolutely irreducible of an univariate polynomial of degrees greater or equal to 2?
    • A. 

      In a linear form

    • B. 

      In a geometric pattern

    • C. 

      By polynomial

    • D. 

      They have no absolutely irreducible value

  • 6. 
    What do we call the decomposition of a multivariate polynomial as a product of absolutely irreducible polynomials?
    • A. 

      Absolute factorization

    • B. 

      Absolute decomposition

    • C. 

      Absolute disintegration

    • D. 

      Absolute computation

  • 7. 
    How do we represent the absolutely irreducible algorithms? 
    • A. 

      Geometric progressions

    • B. 

      Polynomials

    • C. 

      Arithmetic progressions

    • D. 

      Trigonometric rates

  • 8. 
    What are absolutely irreducible polynomials also called?
    • A. 

      Non-constant polynomials

    • B. 

      Constant polynomials

    • C. 

      Random polynomials

    • D. 

      Fractional polynomials

  • 9. 
    What does the property of irreducibility depend on?
    • A. 

      Number of coefficients

    • B. 

      Nature of coefficients

    • C. 

      Type of coefficients

    • D. 

      Value of coefficients

  • 10. 
    What sole condition describes a univariate polynomial that is absolutely irreducible? Its degree must be... 
    • A. 

      4

    • B. 

      3

    • C. 

      2

    • D. 

      1