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Intro to Polynomials quiz

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  • What is the definition of a polynomial?
    A polynomial is an algebraic expression where variables have only positive whole number exponents.
  • Is x^(-2) a polynomial? Why or why not?
    No, because the exponent is negative, and polynomials require positive whole number exponents.
  • What is a monomial?
    A monomial is a polynomial with only one term.
  • How do you determine the number of terms in a polynomial?
    Count the parts of the expression separated by plus or minus signs.
  • Is 3/4 x + x^3 a polynomial? If so, what type?
    Yes, it is a binomial because both terms have positive whole number exponents.
  • Why is 5/y not a polynomial?
    Because it can be rewritten as 5y^(-1), which has a negative exponent.
  • Can a polynomial have more than one variable? Give an example.
    Yes, for example, 2x^3y^2 is a polynomial as long as all exponents are positive whole numbers.
  • What is the degree of a term in a polynomial?
    It is the sum of all the exponents on the variables in that term.
  • How do you find the degree of a polynomial?
    Find the degree of each term and select the highest one.
  • What is the degree of the term x^2y^3?
    The degree is 5, because 2 + 3 = 5.
  • What is the degree of a constant term like 17 in a polynomial?
    The degree is always zero because there are no variables.
  • In the polynomial 5x + 7x^4 - x^2 + 17, what is the degree of the polynomial?
    The degree is 4, which is the highest degree among the terms.
  • What is a binomial?
    A binomial is a polynomial with exactly two terms.
  • How do you determine the degree of the term 18xy^2?
    Add the exponents: 1 (for x) + 2 (for y) = 3.
  • If a term has no exponent written, what exponent is assumed?
    An exponent of 1 is assumed.