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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 (
[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
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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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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