dependent equations Equations of a sys-
tem that have the same graph (because they
are different forms of the same equation) are
called dependent equations. (Section 4.1)
descending powers A polynomial in one
variable is written in descending powers of
the variable if the exponents on the variables
of the terms of the polynomial decrease from
left to right. (Section 5.4)
difference The answer to a subtraction
problem is called the difference. (Section 1.1)
difference of cubes The difference of
cubes, , can be factored as
. (Sec-
tion 6.4)
difference of squares The difference of
squares, , can be factored as
. (Section 6.4)
direct variation yvaries directly as xif
there exists a nonzero real number (constant)
ksuch that. (Section 7.8)
discriminant The discriminant of the quad-
ratic equation is the
quantity under the radical in the
quadratic formula. (Section 9.3)
disjoint sets Sets that have no elements in
common are disjoint sets. (Appendix)
distributive property of multiplication with
respect to addition (distributive property)
For any real numbers a,b, and c, the distribu-
tive property states that
and. (Section 1.7)
domain The set of all first components
(x-values) in the ordered pairs of a relation is
called the domain. (Section 3.6)
elements (members) The elements (mem-
bers) of a set are the objects that belong to
the set. (Section 1.3, Appendix)
elimination method The elimination
method is an algebraic method used to solve a
system of equations in which the equations of
the system are combined so that one or more
variables is eliminated. (Section 4.3)
empty set (null set) The empty set, denoted
by or , is the set containing no elements.
(Section 2.3, Appendix)
equation An equation is a statement that two
algebraic expressions are equal. (Section 1.3)
equivalent equations Equivalent equations
are equations that have the same solution set.
(Section 2.1)
exponent (power) An exponent, or power,
is a number that indicates how many times its
base is used as a factor. In , xis the expo-
nent (power). (Sections 1.2, 5.1)
exponential expression A number or let-
ter (variable) written with an exponent is an
exponential expression. (Sections 1.2, 5.1)
extraneous solution A proposed solution
to an equation, following any of several pro-
cedures in the solution process, that does
not satisfy the original equation is called an
extraneous solution. (Section 8.6)
extremes of a proportion In the propor-
tion , the a- and d-terms are called the
extremes. (Section 2.6)factor Ifa,b, and crepresent numbers and
thanaandbare factors of c.
(Sections 1.1, 6.1)
factored A number is factored by writing
it as the product of two or more numbers.
(Section 1.1)
factored form An expression is in fac-
tored form when it is written as a product.
(Section 6.1)
factoring Writing a polynomial as the
product of two or more simpler polynomials
is called factoring. (Section 6.1)
factoring by grouping Factoring by group-
ing is a method for grouping the terms of a
polynomial in such a way that the polyno-
mial can be factored. It is used when the
greatest common factor of the terms of the
polynomial is 1. (Section 6.1)
factoring out the greatest common factor
Factoring out the greatest common factor is
the process of using the distributive property
to write a polynomial as a product of the
greatest common factor and a simpler poly-
nomial. (Section 6.1)
FOIL FOIL is a mnemonic device which
represents a method for multiplying two
binomials. Multiply First
terms ac,Outer terms ad,Inner terms bc,
andLast terms bd. Then combine like terms.
(Section 5.5)
formula A formula is an equation in which
variables are used to describe a relationship
among several quantities. (Section 2.5)
fourth root A number bis a fourth root of
aif is true. (Section 8.1)
function A function is a set of ordered pairs
(x,y) in which each value of the first compo-
nentxcorresponds to exactly one value of the
second component y. (Section 3.6)
function notation If a function is denoted
by ƒ, the notation is called func-
tion notation. Here y, or , represents the
value of the function at x. (Section 3.6)graph of a number The point on a number
line that corresponds to a number is its graph.
(Section 1.4)
graph of an equation The graph of an
equation in two variables is the set of all points
that correspond to all of the ordered pairs that
satisfy the equation. (Section 3.2)
graphing method The graphing method
for solving a system of equations requires
graphing all equations of the system on the
same axes and locating the ordered pair(s) of
their intersection. (Section 4.1)
greatest common factor (GCF) The great-
est common factor of a list of integers is
the largest factor of all those integers. The
greatest common factor of the terms of a
polynomial is the largest factor of all the
terms in the polynomial. (Sections 1.1, 6.1)
grouping symbols Examples of grouping
symbols are parentheses , brackets ,
and fraction bars. (Section 1.2)hypotenuse The side opposite the right
angle in a right triangle is the longest side and
is called the hypotenuse. (Section 6.6)identity An identity is an equation that is
true for all valid replacements of the vari-
able. It has an infinite number of solutions.
(Section 2.3)
identity element for addition For all real
numbersa, The num-
ber 0 is called the identity element for
addition. (Section 1.7)
identity element for multiplication For all
real numbers a, The
number 1 is called the identity element for
multiplication. (Section 1.7)
identity property The identity property
for addition states that the sum of 0 and any
number equals the number. The identity prop-
erty for multiplication states that the product
of 1 and any number equals the number.
(Section 1.7)
imaginary part The imaginary part of the
complex number is b. (Section 9.4)
inconsistent system An inconsistent sys-
tem of equations is a system with no solution.
(Section 4.1)
independent equations Equations of a
system that have different graphs are called
independent equations. (Section 4.1)a+bia# 1 = 1 #a=a.
a+ 0 = 0 +a=a.I
H
12 34G
ƒ 1 x 2y=ƒ 1 x 2b^4 =a1 a+b 21 c+d 2a#b=c,
F
a
b=
c
dbx560E
1 b+c 2 a=ba+caa 1 b+c 2 =ab+acb^2 - 4 acax^2 +bx+c= 0y=kxx^2 - y^2 = 1 x+y 21 x-y 2
x^2 - y^2x^3 - y^3 = 1 x-y 21 x^2 +xy+y^22
x^3 - y^3G-2 Glossary
http://www.ebook777.com
http://www.ebook777.com