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- 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 (
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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 (
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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 (
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An
equation is a statement that two expressions are equal.
Numerical evaluation (
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Numerical evaluation is the process of determining a value by substituting numbers for letters.
Polynomials (
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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 (
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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
(
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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 (
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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
classification of plants, gymnosperm features.
what is the features of gymnosperm
Linsy
how many types of solid did we have
what is an ionic bond
Samuel
what is fallopian tube
Merolyn
what's bulbourethral gland
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium
Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ.
The term pathogen came into use in the 1880s.[1][2
Zainab
Definition of respiration
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
what are the functions of follicle stimulating harmones?
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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