# Key Terms Chapter 05: Polynomials and Polynomial Functions

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Example and Directions
Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
(Eg. "Genetic, Hereditary, DNA ...")(Eg. "Relating to genes or heredity") The infamous double helix https://bio.libretexts.org/CC-BY-SA; Delmar Larsen
Glossary Entries
binomialA binomial is a polynomial with exactly two terms.
conjugate pairA conjugate pair is two binomials of the form $$(a−b), (a+b)$$. The pair of binomials each have the same first term and the same last term, but one binomial is a sum and the other is a difference.
degree of a constantThe degree of any constant is $$0$$.
degree of a polynomialThe degree of a polynomial is the highest degree of all its terms.
degree of a termThe degree of a term is the sum of the exponents of its variables.
monomialA monomial is an algebraic expression with one term. A monomial in one variable is a term of the form $$ax^m$$, where $$a$$ is a constant and $$m$$ is a whole number.
polynomialA monomial or two or more monomials combined by addition or subtraction is a polynomial.
polynomial functionA polynomial function is a function whose range values are defined by a polynomial.
Power PropertyAccording to the Power Property, $$a$$ to the $$m$$ to the $$n$$ equals $$a$$ to the $$m$$ times $$n$$.
Product PropertyAccording to the Product Property, $$a$$ to the $$m$$ times $$a$$ to the $$n$$ equals $$a$$ to the $$m$$ plus $$n$$.
Product to a PowerAccording to the Product to a Power Property, $$a$$ times $$b$$ in parentheses to the $$m$$ equals $$a$$ to the $$m$$ times $$b$$ to the $$m$$.
Properties of Negative ExponentsAccording to the Properties of Negative Exponents, $$a$$ to the negative $$n$$ equals $$1$$ divided by $$a$$ to the $$n$$ and $$1$$ divided by $$a$$ to the negative $$n$$ equals $$a$$ to the $$n$$.
Quotient PropertyAccording to the Quotient Property, $$a$$ to the $$m$$ divided by $$a$$ to the $$n$$ equals $$a$$ to the $$m$$ minus $$n$$ as long as $$a$$ is not zero.
Quotient to a Negative ExponentRaising a quotient to a negative exponent occurs when $$a$$ divided by $$b$$ in parentheses to the power of negative $$n$$ equals $$b$$ divided by $$a$$ in parentheses to the power of $$n$$.
Quotient to a Power PropertyAccording to the Quotient to a Power Property, $$a$$ divided by $$b$$ in parentheses to the power of $$m$$ is equal to $$a$$ to the $$m$$ divided by $$b$$ to the $$m$$ as long as $$b$$ is not zero.
standard form of a polynomialA polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.
trinomialA trinomial is a polynomial with exactly three terms.
Zero Exponent PropertyAccording to the Zero Exponent Property, $$a$$ to the zero is $$1$$ as long as $$a$$ is not zero.