It is our goal to provide you with just the right amount of critical
informaion to put you on the path to better Algebra Grades without
hitting you with the information overload that is so common on the
internet.
This is not an Algebra Encyclopedia - No information overload - just the
basics.
Our Algebra Dictionary has been organized in an alphabetical listing of the
algebra terms defined. For your convenience the terms are also divided
into three groups (A-I, J-R and S-Z). Many of the algebra terms listed in
our Algebra Dictionary are also linked to a separate page with examples if
you want to know more. Just click on the underlined terms to be taken
from the Algebra Dictonary to specific pages which explain the terms in
more detail.
Zero of a Polynomial
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Algebra Dictionary A thru I
A
Algebra
Algebra - Algebra is simply doing arithmetic with at least one number
replaced by a letter, which is referred to as an unknown and can be
either a variable or a constant. For example, you know how to do 3 + 2 =
5. This is arithmetic. If we replace 2 with x we have 3 + x = 5. We
know just from looking at this that x = 2. Algebra is simply a set of
rules to find out the value of x.
Algebra Equations
Algebra Equations - An arithmetic or algebra equation is simply an
arithmetic or algebra expression with an = sign. For example the
arithmetic equations 3 + 2 = 5 or 3 * 5 = 15 and the algebra equations 3
+ x =5 or 3 * x = 15.
Algebra Expressions
Algebra Expressions - An arithmetic expression is a sequence of numbers
and operations such as 3 + 2 or 3 * 5 or 6 / 3. (Note that we DO NOT use
the symbol x to indicate multiplication because in algebra x is
frequently used as an unknown or variable). An algebra expression is a
sequence of numbers, letters and operations such as 3+x or 3 * x
or x / 3.
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B
Binomials
Binomials - Binomials are algebra expressions with only two terms, such
as x + 1, y - 5 or 4*x.
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C
Cartesian Coordinates
Cartesian Coordinates, sometimes called
Rectangular Coordinates, are named after the French mathematician Rene'
Descartes who developed this system of graphically representing any
point uniquely in a plane by two numbers, usually x and y. The
coordinates consist of two lines intersecting perpendicular to one
another. These lines are referred to as the x-axis and the y-axis. Any
point on the rectangular plane defined by the two lines can be
represented by a combination of distances along the x and y axes.
Cartesian Plane
A plane is a two dimensional surface which has
infinite width, infinite length and zero thickness. The plane created
by the x and y axes of the Cartesian Coordinates is referred to as the
Cartesian Plane.
Completing the Square
One of the four methods of solving Quadratic
Equations. Completing the Square is a method in which terms are added
to both sides of the general Quadratic Equation ax2 + bx + c
= 0 where a, b and c are constants, such that the resulting expression
on the left side is a perfect square of a given binomial.
Constants
As discussed previously, Algebra involves doing arithmetic
with numbers and letters (for example 3 + x = 5) The letters are
referred to as unknowns. Sometimes the letters can take on a
variety of values and are called variables. Other times the
letters have an unknown but fixed value and are called constants.
Coordinate Plane
See Cartesian Plane
Cube Root
The cube root of a given number is the unique number that
when raised to the 3rd power (multiplied by itself 3 times) will equal
the original given number.
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D
Domain
The domain of a function consists of all real values of x that
yield real values of y when the domain values of x are substituted for x
in the function.
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E
Exponent
In arithmetic an exponent is represented by a base number
with a super scripted number such as 23. The base number in
this case is 2 and the exponent is 3. The exponent is the number of
times the base is multiplied by itself. In our example 23 =
2 * 2 * 2 = 8. In Algebra, the base is usually an unknown or a variable
such as x. In this case our equation would become x3 = x * x
* x.
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F
FOIL Method
The FOIL Method is an acronym that helps us remember how
to multiply together two binomials. For instance the (x + 2) * (x + 3).
The FOIL Method consists of multiplying the First two terms
(x*x), then multiplying the Outermost terms (x*3), then
multiplying the I>nnermost two terms (2*x), then multiplying the
Last two terms (2*3) and finally adding all the product together.
The result is the following: (x + 2) * (x + 3) = x2 + 3*x +
2*x + 2*3 which can be combined to give x2 + 5*x + 6.
Function
A function is an algebra equation in which there are two
variables such as y = 2*x + 3. From this equation we see that the
variable y changes as x changes. When x = 1 then y = 2*1 + 3 which is 5.
When x = 2 then y = 2*2 +3 which is 7. Y is said to vary as a function of x
and is sometimes written as y = f(x) [read as "y = a function of x"].
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G
Graph Paper
A paper that has lines running parallel to both the x and
y axes in the Cartesian Plane. The spacing between the lines is equal to
a specific, defined distance on each axis.
Graphing Functions
Graphing Functions consists of locating each unique
value of x and y of the function y = f(x) and placing a point at that
location on the Cartesian Plane.
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Algebra Dictionary J thru R
L
Linear Equations
Linear Equations, sometimes referred to as
Linear Functions, are polynomials of the first order that contain
only x to the first power and constants and have a general form of
ax + b = 0 where a and b are constants.
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M
Monomial
A Monomial is an algebra expression with only one term, such
as x, y or 4*x.
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O
Operations
Operations in Algebra are the same as those in arithmetic.
The common operations are exponentiation, multiplication, division,
addition and subtraction.
Order of Operations
In Algebra as in arithmetic, to get the correct
answer the mathematical operations much be carried out in a specific
order. An acronym to help remember this required order is PEMDAS -
First, carryout all operations contained within Parentheses
(NOTE: The order of operations must be observed within the
parenthesis). Second, do Exponents. Third, do
Multiplication. Fourth, do Division. Fifth, do
Addition. And last, do Subtraction.
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P
Polynomial
A Polynomial is an algebra expression with more than two
terms. Examples of Polynomials include: x2 - 2*x + 1 and
x3 + 2 * x2 + 3 * x + 5. Polynomials are defined
by their order or degree which is the highest power of x present int he
polynomial.
A polynomial of zero order or degree 0 is simply a constant number. A
polynomial of the first order or degree 1 is a linear equation
(containing only x to the first power) such as y = ax + b where a and b
are constants. A polynomial of the second order or degree 2 is a
quadratic equation (containing only x to the first and second powers)
such as ax2 + bx + c where a, b and c are constants.
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Q
Quadrants
Quadrants are the result of dividing the Cartesian Plane
into four equal parts. You can think of the Cartesian Plane as being
represented by a pie cut into four equal pieces. The Northeast piece is
referred to as Quadrant 1 or Q1. The Northwest piece is referred to as
Quadrant 2 or Q2. the Southwest piece is referred to as Quadrant 3 or
Q3. The Southeast piece is referred to as Quadrant 4 or Q4. So the four
Quadrants of the Cartesian Plane proceed counterclockwise from Q1 to Q4.
Quadratic Equations
Quadratic Equations, sometimes referred to as
Quadratic Functions, are polynomials of the second order that contain
only x to the first and second power and have a general form of
ax2 + bx + c = 0 where a, b and c are constants.
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R
Range
The range of a function consists of all real values of y that
result when the domain values of x are substituted for x
in the function.
Rectangular Coordinates
See Cartesian Coordinates
Root of a Polynomial
A solution to an algebra equation in which a polynomial equals
zero is called a root of the polynomial. The root of a polynomial
is sometimes referred to as a zero of the polynomial.
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Algebra Dictionary S thru Z
S
Scientific Notation
Scientific Notation is a method of representing
very large and very small numbers as a product of the number multiplied
by a power of 10. For example, the number 1,000 in Scientific Notation
is 1.0 * 103 and the number 0.001 in Scientific Notation is
1.0 * 10-3.
Set Theory
Set Theory can get pretty complicated when looked at from a
mathematician's viewpoint. In Algebra, Set Theory is mainly used to
define the domain and range of a function. In general, a set is defined
as a group of objects. More simply, in Algebra we define a set as the x
values or y values that make up the domain and range of a function.
There are various ways of expressing sets. These include using
graphical, number-line representations and specific Set Theory
nomenclature.
Significant Figures
The number of significant figures a given number
or value has defines the accuracy of the measurement used to generate
the number. For example, if a piece of pipe is measured at approximately
3 feet then the length has only one significant number. However, if a
very accurate digital measuring device is used and the pipe is actually
measured to the nearest 1/100 of an foot to be 3.24 ft then the length
has 3 significant figures. There are specific and different rules for
determining the number of significant figures when measurements are used
in the various operations such as multiplication and addition.
Solving Quadratic Equations
A Quadratic Equation is an algebra
equation of the general form ax2 + bx + c = 0 where a, b and
c are constants. There are four main methods of solving quadratic
equations: 1) Extracting Roots; 2) Factoring; 3) Completing the Square;
and 4) using the Quadratic Formula.
Square Root
The square root of a given number is the unique number that
when raised to the 2nd power (multiplied by itself) will equal
the original given number.
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U
Units of Measure
Units of measure are specific quantifications that
give physical meaning to numbers representing measurements. For
example, if I told you an oak tree was 60 high you would not know
whether the tree was a seedling, a sprout or a might oak tree. So we
have to assign some unit of measure to make a numerical measurement
meaningful. In this instance if we have a tree that measures 60
millimeters it is a seedling. It it measures 60 inches it is a sprout.
If it measures 60 meters it is indeed a mighty oak.
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V
Variables
As discussed previously, Algebra involves doing arithmetic
with numbers and letters (for example 3 + x = 5) The letters are
referred to as unknowns. Sometimes the letters can take on a
variety of values and are called variables. Other times the
letters have an unknown but constant value and are called constants.
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Z
Zero of a Polynomial
A solution to an algebra equation in which a polynomial equals
zero is called a zero of the polynomial. The zero of a polynomial
is sometimes referred to as a root of the polynomial.
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