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Intro to Polynomials definitions

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  • Polynomial
    An algebraic expression with variables raised only to positive whole number exponents, possibly involving multiple terms.
  • Monomial
    A single-term algebraic expression where the variable exponents are positive whole numbers.
  • Binomial
    An algebraic expression consisting of exactly two terms, each with variables raised to positive whole number exponents.
  • Trinomial
    An algebraic expression made up of three terms, each separated by plus or minus signs.
  • Term
    A part of an algebraic expression separated by addition or subtraction, often containing variables and coefficients.
  • Exponent
    A number indicating how many times a variable is multiplied by itself in an algebraic expression.
  • Coefficient
    A numerical factor placed in front of a variable or term in an algebraic expression.
  • Degree
    The sum of all exponents on the variables within a single term or the highest such sum in a polynomial.
  • Constant
    A term in an algebraic expression that contains no variables; its degree is always zero.
  • Multivariable Polynomial
    An algebraic expression with more than one variable, each raised to positive whole number exponents.
  • Algebraic Expression
    A mathematical phrase combining numbers, variables, and operations, but not containing an equals sign.
  • Positive Whole Number
    A counting number greater than zero, used as an exponent in valid polynomial expressions.
  • Fractional Exponent
    An exponent that is a fraction, which disqualifies an expression from being a polynomial.
  • Negative Exponent
    An exponent less than zero, which prevents an expression from being classified as a polynomial.
  • Invisible One
    An implied exponent of one on a variable when no exponent is written, common in algebraic expressions.