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Polynomials Intro 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.
  • Why is 2x^-3 not considered a polynomial?
    Because it has a negative exponent, and polynomials require only positive whole number exponents.
  • What do the prefixes mono-, bi-, and tri- mean in the context of polynomials?
    Mono- means one term (monomial), bi- means two terms (binomial), and tri- means three terms (trinomial).
  • How are terms in a polynomial separated?
    Terms in a polynomial are separated by plus or minus signs.
  • Is 5/y a polynomial? Why or why not?
    No, because it can be rewritten as 5y^-1, which has a negative exponent.
  • Can a polynomial have more than one variable?
    Yes, as long as all exponents on the variables are positive whole numbers.
  • What is the standard form of a polynomial?
    Standard form requires terms to be written in descending order of exponents, with all like terms combined.
  • What is the degree of a polynomial?
    The degree is the highest exponent of the variable in the polynomial.
  • What is the leading coefficient of a polynomial?
    It is the coefficient of the term with the highest exponent in the polynomial.
  • How do you add polynomials?
    By combining like terms, matching variables and exponents, and writing the result in standard form.
  • What must you be careful of when subtracting polynomials?
    You must distribute the negative sign to all terms in the polynomial being subtracted before combining like terms.
  • If a polynomial has the terms 3x^2 + 5x + 4, what is its degree and leading coefficient?
    The degree is 2, and the leading coefficient is 3.
  • What happens if you add 5x^2 + 2x + 3 and x^2 + 7x + 8?
    You get 6x^2 + 9x + 11 after combining like terms.
  • How do you write 1/2x + x^3 in standard form?
    Rewrite it as x^3 + 1/2x, with the highest exponent first.
  • What is the result of subtracting (5x + 10 - x^2) from (3x^2 + 2x + 4)?
    The result is 4x^2 - 3x - 6 after distributing the negative and combining like terms.