-
Home
- Elementary algebra
- Algebraic expressions and
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.This module contains a summary of the key concepts in the chapter "Algebraic Expressions and Equations".
Summary of key concepts
Algebraic expressions (
[link] )
An
algebraic expression (often called simply an expression) is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation. (
is not meaningful.)
In an algebraic expression, the quantities joined by "
" signs are
terms .
Distinction between terms and factors (
[link] )
Terms are parts of sums and are therefore separated by addition signs.
Factors are parts of products and are therefore separated by multiplication signs.
Common factors (
[link] )
In an algebraic expression, a factor that appears in
every term, that is, a factor that is common to each term, is called a
common factor .
Coefficients (
[link] )
The
coefficient of a quantity records how many of that quantity there are. The coefficient of a group of factors is the remaining group of factors.
Distinction between coefficients and exponents (
[link] )
Coefficients record the number of like terms in an expression.
Exponents record the number of like factors in an expression
Equation (
[link] )
An
equation is a statement that two expressions are equal.
Numerical evaluation (
[link] )
Numerical evaluation is the process of determining a value by substituting numbers for letters.
Polynomials (
[link] )
A polynomial is an algebraic expression that does not contain variables in the denominators of fractions and in which all exponents on variable quantities are whole numbers.
A
monomial is a polynomial consisting of only one term.
A
binomial is a polynomial consisting of two terms.
A
trinomial is a polynomial consisting of three terms.
Degree of a polynomial (
[link] )
The degree of a term containing one variable is the value of the exponent on the variable.
The degree of a term containing more than one variable is the sum of the exponents on the variables.
The degree of a polynomial is the degree of the term of the highest degree.
Linear quadratic cubic polynomials (
[link] )
Polynomials of the first degree are
linear polynomials.
Polynomials of the second degree are
quadratic polynomials.
Polynomials of the third degree are
cubic polynomials.
Like terms (
[link] )
Like terms are terms in which the variable parts, including the exponents, are identical.
Descending order (
[link] )
By convention, and when possible, the terms of an expression are placed in descending order with the highest degree term appearing first.
is in descending order.
Multiplying a polynomial by a monomial (
[link] )
To multiply a polynomial by a monomial, multiply every term of the polynomial by the monomial and then add the resulting products together.
Simplifying
And
(
[link] )
Multiplying a polynomial by a polynomial (
[link] )
To multiply polynomials together, multiply every term of one polynomial by every term of the other polynomial.
Special products (
[link] )
Independent and dependent variables (
[link] )
In an equation, any variable whose value can be freely assigned is said to be an
independent variable . Any variable whose value is determined once the other values have been assigned is said to be a
dependent variable .
The collection of numbers that can be used as replacements for the independent variable in an expression or equation and yield a meaningful result is called the
domain of the expression or equation.
Questions & Answers
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
hey , can you please explain oxidation reaction & redox ?
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
advantages of electrons in a circuit
we're do you find electromagnetism past papers
Ntombifuthi
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is the half reaction of Potassium and chlorine
how to calculate coefficient of static friction
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
How is energy being used in bonding?
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
how to calculate tension by substitution
use fnet method. how many obects are being calculated ?
Khuthadzo
how to calculate acceleration and tension force
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
how to calculate normal force
Mulaudzi
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.