Classifying Polynomials Flashcards

Classifying Polynomials

• Monomial: An expression consisting of a single term.
• Binomial: An expression containing two distinct terms.
• Trinomial: An expression made up of three individual terms.
• Polynomial: Comprises one or more monomials, can be expressed as their sum or difference.
• Constant: A polynomial with a degree of zero; it is a single numerical value.
• Linear Polynomial: Defined by a degree of 1, indicated by a linear equation.
• Quadratic Polynomial: Resides at degree 2, typically taking the form of a parabola.
• Cubic Polynomial: Represents degree 3, often featuring inflection points in its graph.
• Quartic Polynomial: Identified by a degree of 4, it can have up to four roots.
• Quintic Polynomial: Denotes degree 5, can exhibit complex behaviors in graphs.
• Nth Degree Polynomial: Any polynomial with a degree higher than 5; classified based on its highest degree term.
• Degree of a Monomial: Obtained by summing the exponents of all variables present.
• Degree of a Polynomial: Identified by the term with the highest degree within the polynomial.
• Leading Coefficient: The coefficient associated with the polynomial's first term when in standard form.
• Standard Form of a Polynomial: A conventional arrangement that lists terms in descending order of degree.
• Examples:
  • Monomial: 5a³b²c with a degree of 6 (3+2+1).
  • Quadratic Binomial: 4x - 2x² with degree 2.
  • Cubic Trinomial: 5a³ - 4a - 6 with degree 3.
  • Quintic Polynomial: 4x² - 3x + 2x⁵ - 7 + 3x³ with a degree of 5.
  • Quartic Monomial: -12m²n² with a degree of 4.
  • Constant: The number 12 is a polynomial of degree zero.
• Example Linear Monomial: 4x, characterized by a degree of 1.