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

what does preconceived mean

sammie Reply

physiological Psychology

Nwosu Reply

How can I develope my cognitive domain

Amanyire Reply

why is communication effective

Dakolo Reply

Communication is effective because it allows individuals to share ideas, thoughts, and information with others.

effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.

it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.

miss

Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment

Wekolamo Reply

please i need answer

Wekolamo

because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).

Manix Reply

Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!

ARC

A child is a member of community not society elucidate ?

JESSY Reply

Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?

Simon Reply

compare and contrast skinner's perspective on personality development on freud

namakula Reply

Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning

war

explain how nature and nurture affect the development and later the productivity of an individual.

Amesalu Reply

nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.

Samuel

I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills

Zyryn Reply

good👍

Jonathan

and having a good philosophy of the world is like a sandwich and a peanut butter 👍

Jonathan

generally amnesi how long yrs memory loss

Kelu Reply

interpersonal relationships

Abdulfatai Reply

What would be the best educational aid(s) for gifted kids/savants?

Heidi Reply

treat them normal, if they want help then give them. that will make everyone happy

Saurabh

What are the treatment for autism?

Magret Reply

hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these

Jharna

continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child

Jharna

child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective

Jharna

results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.

Jharna

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

	39 Biology 39 The Respiratory System MCQ By OpenStax Start Quiz
	13 Sociology 13 Aging and the Elderly MCQ By OpenStax Start Quiz
	Cultural Evolution Contemporary World By Richley Crapo Start Assignment
©flickr: brett	Celine Dion Quiz By JavaChamp Team Start Quiz
	Pre-class Online Quiz - Case Control Studies By Mucho Mizinduko Start Quiz
©flickr: Justin	The Last Holiday Concert Chapter 1 By Mackenzie Wilcox Start Quiz
	Human A&P 2- Final By Madison Christian Start Flashcards
©flickr: Urko	Music Reviewer MCQ By Edgar Delgado Start Quiz
©flickr: Mike	Examples of Wiffle IQ By Sean WiffleBoy Start Quiz
	10 Biology 10 Cell Reproduction MCQ By OpenStax Start Quiz

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] )