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Binomial Theorem Quiz
10 Questions
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Binomial Theorem Quiz

Created by
@NeatPine

Questions and Answers

What does the binomial theorem describe in elementary algebra?

  • The multiplication of two binomials
  • The algebraic expansion of powers of a binomial (correct)
  • The simplification of binomial expressions
  • The factorization of binomial expressions

    • In the binomial theorem, what are the exponents b and c required to be?

  • Any real numbers
  • Nonnegative integers (correct)
  • Both positive integers
  • Both negative integers

    • What is the coefficient 'a' in the term axbyc known as?

  • Binomial coefficient (correct)
  • Binomial factor
  • Combination coefficient
  • Exponential coefficient

    • What is the binomial coefficient ( n b ) or ( n c ) used for in the context of the binomial theorem?

    <p>Determining the number of different combinations of b elements that can be chosen from an n-element set</p> Signup and view all the answers

    When were special cases of the binomial theorem known as per the given text?

    <p>In the 4th century BC</p> Signup and view all the answers

    What do the numbers ( n b ) or ( n c ) represent in the context of the binomial theorem?

    <p>Number of different combinations of b elements that can be chosen from an n-element set</p> Signup and view all the answers

    What is the purpose of arranging binomial coefficients for varying n and b to form Pascal's triangle?

    <p>Facilitating calculations in combinatorics</p> Signup and view all the answers

    According to the binomial theorem, how is it possible to expand the polynomial (x + y)n?

    <p>Into a sum involving terms of the form axbyc</p> Signup and view all the answers

    What is the historical significance of Greek mathematician Euclid's mention of the special case of the binomial theorem for exponent 2?

    <p>It provides evidence of early knowledge of the binomial theorem</p> Signup and view all the answers

    What does Indian mathematician Aryabhata's method for finding cube roots suggest about his knowledge?

    <p>He knew the binomial formula for exponent 3</p> Signup and view all the answers

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