Intermediate Algebra 2e

# Key Terms

binomial
A binomial is a polynomial with exactly two terms.
conjugate pair
A conjugate pair is two binomials of the form $(a−b),(a+b).(a−b),(a+b).$ 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 $axm,axm,$ 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.