Polynomial Vocabulary Study Notes

Polynomial Vocabulary Study Notes

• Term: Represents individual components in a polynomial, separated by plus or minus signs.
• Factor: Elements that multiply to produce a number or expression; a factor divides its corresponding number without a remainder.
• Monomial: A polynomial consisting of only one term.
• Binomial: A polynomial composed of two distinct terms.
• Polynomial: An expression formed by summing or subtracting multiple terms, where each term contains variables raised to positive integer exponents.
• Leading Coefficient: The coefficient of the term with the highest degree within a polynomial, indicating its growth rate.
• Constant Term: The term that remains after variables are eliminated, essentially a standalone number.
• Degree of the Polynomial: Identifies the highest exponent in the polynomial, indicating its overall degree.
• Standard Form: A format where polynomial terms are organized from highest to lowest exponent, providing clarity on the polynomial's degree.
• Trinomial: A polynomial made up of three separate terms.
• Quadratic: Refers to polynomials (or functions) that have a degree of 2, typically resulting in a parabolic graph.
• Cubic: Denotes polynomials with a degree of 3, producing S-shaped graphs.
• Zeros: Real solutions to a polynomial equation; also defined as the x-intercepts of its graph.
• Quartic: A polynomial function characterized by a degree of 4, exhibiting complex curves.
• Roots: Solutions for polynomial equations, which may include both real and imaginary numbers.
• End Behavior: Describes the trend of a polynomial's graph as the input value approaches positive or negative infinity, indicating how the graph behaves in extreme values.
• Turning Points: Points on the graph where the polynomial function transitions between increasing and decreasing; can represent hills or valleys in the graph.