4.8 Summary of key concepts

Elementary algebra Page 1 / 1

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. (

5 \div 0

is not meaningful.)

Terms ( [link] )

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.

\underset{3 terms}{\underset{︸}{x + x + x}} = \underset{coefficient is 3}{3 x}

Exponents record the number of like factors in an expression

\underset{3 factors}{\underset{︸}{x \cdot x \cdot x}} = \underset{exponent is 3}{x^{3}}

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.

5 x^{3} - 2 x^{2} + 10 x - 15

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.

7 (x - 3) = 7 x - 7 \cdot 3 = 7 x - 21

Simplifying $+ (a + b)$ And $- (a + b)$ ( [link] )

\begin{array}{l} + (a + b) = a + b \\ - (a + b) = - a - b \end{array}

Multiplying a polynomial by a polynomial ( [link] )

To multiply polynomials together, multiply every term of one polynomial by every term of the other polynomial.

\begin{array}{l} (x + 3) (x - 4) & = & x^{2} - 4 x + 3 x - 12 \\ = & x^{2} - x - 12 \end{array}

Special products ( [link] )

\begin{matrix} {(a + b)}^{2} & = & a^{2} + 2 a b + b^{2} & N o t e : & {(a + b)}^{2} & \neq & a^{2} + b^{2} \\ {(a - b)}^{2} & = & a^{2} - 2 a b + b^{2} & {(a - b)}^{2} & \neq & a^{2} - b^{2} \\ (a + b) (a - b) & = & a^{2} - b^{2} \end{matrix}

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 .

Domain ( [link] )

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

summarize halerambos & holbon

David Reply

the Three stages of Auguste Comte

Clementina Reply

what are agents of socialization

Antonio Reply

sociology of education

Nuhu Reply

definition of sociology of education

Nuhu

what is culture

Abdulrahim Reply

shared beliefs, values, and practices

AI-Robot

What are the two type of scientific method

ogunniran Reply

I'm willing to join you

Aceng Reply

what are the scientific method of sociology

Man

what is socialization

ogunniran Reply

the process wherein people come to understand societal norms and expectations, to accept society's beliefs, and to be aware of societal values

AI-Robot

scientific method in doing research

ogunniran

defimition of sickness in afica

Anita

Cosmology

ogunniran

Hmmm

ogunniran

list and explain the terms that found in society

REMMY Reply

list and explain the terms that found in society

Mukhtar

what are the agents of socialization

Antonio

Family Peer group Institution

Abdulwajud

I mean the definition

Antonio

ways of perceived deviance indifferent society

Naomi Reply

reasons of joining groups

SAM

to bring development to the nation at large

Hyellafiya

entails of consultative and consensus building from others

Gadama

World first Sociologist?

Abu

What is evolutionary model

Muhammad Reply

Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u

faruk

what are the modern trends in religious behaviours

Selekeye Reply

what are social norms

Daniel Reply

shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society

Lucius

that is how i understood it

Lucius

examples of societal norms

Diamond

Discuss the characteristics of the research located within positivist and the interpretivist paradigm

Tariro Reply

what is Industrialisation

Selekeye Reply

industrialization

Angelo

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

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.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	25 AP 25 Urinary System MCQ By OpenStax Start Quiz
	SCJP Online Exam 310-065 By Prateek Ashtikar Start Quiz
	24 AP 24 Metabolism Nutrition Essay By OpenStax Start Flashcards
	11 Neuroanatomy 11 The Cerebellum By Stephen Voron Start Quiz
	Time and Stress Management MCQ By Dionne Mahaffey Start Quiz
	2 Muscular System MCQ By Nick Swain Start Quiz
	OOP with Java - Quiz 1 By Vongkol HENG Start Quiz
©flickr: Derek	Treatment Of Psychological Disorders By Michael Nelson Start Quiz
	Spanish Lesson 4 By Anonymous User Start Quiz
	Understanding basic music theory By OpenStax Read Online Course

4.8 Summary of key concepts

Summary of key concepts

Algebraic expressions ( [link] )

Terms ( [link] )

Distinction between terms and factors ( [link] )

Common factors ( [link] )

Coefficients ( [link] )

Distinction between coefficients and exponents ( [link] )

Equation ( [link] )

Numerical evaluation ( [link] )

Polynomials ( [link] )

Degree of a polynomial ( [link] )

Linear quadratic cubic polynomials ( [link] )

Like terms ( [link] )

Descending order ( [link] )

Multiplying a polynomial by a monomial ( [link] )

Simplifying + ( a + b ) And − ( a + b ) ( [link] )

Multiplying a polynomial by a polynomial ( [link] )

Special products ( [link] )

Independent and dependent variables ( [link] )

Domain ( [link] )

Questions & Answers

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Simplifying $+ (a + b)$ And $- (a + b)$ ( [link] )