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Key Terms Chapter 05: Polynomials and Polynomial Functions

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    102246
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    Glossary Entries
    Word(s)DefinitionImageCaptionLinkSource
    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.    
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