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Mathematics LibreTexts

Key Terms Chapter 05: Polynomials and Polynomial Functions

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

conjugate pair | A conjugate pair is two binomials of the form (ab),(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 axm, 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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