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Intermediate Algebra 1e (OpenStax)
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Key Terms Chapter 05: Polynomials and Polynomial Functions

Key Terms Chapter 05: Polynomials and Polynomial Functions

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May 16, 2022
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- Key Terms Chapter 04: Systems of Linear Equations
- Key Terms Chapter 06: Factoring

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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
Word(s)	Definition	Image	Caption	Link	Source
binomial	A binomial is a polynomial with exactly two terms.
conjugate pair	A 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 constant	The degree of any constant is $0$ .
degree of a polynomial	The degree of a polynomial is the highest degree of all its terms.
degree of a term	The degree of a term is the sum of the exponents of its variables.
monomial	A 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.
polynomial	A monomial or two or more monomials combined by addition or subtraction is a polynomial.
polynomial function	A polynomial function is a function whose range values are defined by a polynomial.
Power Property	According to the Power Property, $a$ to the $m$ to the $n$ equals $a$ to the $m$ times $n$ .
Product Property	According to the Product Property, $a$ to the $m$ times $a$ to the $n$ equals $a$ to the $m$ plus $n$ .
Product to a Power	According 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 Exponents	According 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 Property	According 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 Exponent	Raising 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 Property	According 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 polynomial	A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.
trinomial	A trinomial is a polynomial with exactly three terms.
Zero Exponent Property	According to the Zero Exponent Property, $a$ to the zero is $1$ as long as $a$ is not zero.

binomial | A binomial is a polynomial with exactly two terms.

conjugate pair | A 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 constant | The degree of any constant is $0$ .

degree of a polynomial | The degree of a polynomial is the highest degree of all its terms.

degree of a term | The degree of a term is the sum of the exponents of its variables.

monomial | A 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.

polynomial | A monomial or two or more monomials combined by addition or subtraction is a polynomial.

polynomial function | A polynomial function is a function whose range values are defined by a polynomial.

Power Property | According to the Power Property, $a$ to the $m$ to the $n$ equals $a$ to the $m$ times $n$ .

Product Property | According to the Product Property, $a$ to the $m$ times $a$ to the $n$ equals $a$ to the $m$ plus $n$ .

Product to a Power | According 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 Exponents | According 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 Property | According 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 Exponent | Raising 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 Property | According 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 polynomial | A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.

trinomial | A trinomial is a polynomial with exactly three terms.

Zero Exponent Property | According to the Zero Exponent Property, $a$ to the zero is $1$ as long as $a$ is not zero.

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