- Algebraic Expressions
- Terms and Factors
- Common Factors
- Coefficients

Inside Collection (Textbook): Basic Mathematics Review

Summary: 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. Objectives of this module: be familiar with algebraic expressions, understand the difference between a term and a factor, be familiar with the concept of common factors, know the function of a coefficient.

- Algebraic Expressions
- Terms and Factors
- Common Factors
- Coefficients

An algebraic expression is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation.

Algebraic expressions are often referred to simply as *expressions*, as in the following examples:

The number 8 is an expression. 8 can be written with explicit signs of operation by writing it as

*not* an expression, it is an *equation*. We will study equations in the next section.

In an algebraic expression, the quantities joined by

In some expressions it will appear that terms are joined by

An important concept that all students of algebra must be aware of is the difference between *terms* and *factors*.

Any numbers or symbols that are multiplied together are factors of their product.

Terms are parts of *sums* and are therefore joined by addition (or subtraction) signs.

Factors are parts of *products* and are therefore joined by multiplication signs.

Identify the terms in the following expressions.

This expression has four terms:

In this expression there is only one term. The term is

In this expression there are two terms: the terms are

Using our definition of subtraction, this expression can be written in the form

Rather than rewriting the expression when a subtraction occurs, we can identify terms more quickly by associating the

Associating the sign with the individual quantities we see that the terms of this expression are

Let’s say it again. The difference between terms and factors is that terms are joined by

signs and factors are joined by

signs.

addition, multiplication

List the terms in the following expressions.

Identify the factors in each term.

In the expression

first term:

second term:

third term:

8,

In the expression

first term:

second term:

10 and 1 or 5 and 2; 2,

Sometimes, when we observe an expression carefully, we will notice that some particular factor appears in every term. When we observe this, we say we are observing *common factors*. We use the phrase *common factors* since the particular factor we observe is common to all the terms in the expression. The factor appears in each and every term in the expression.

Name the common factors in each expression.

The factor

The factor

The only factor common to all three terms is the number 3. (Notice that

The factor

The number 5, the

There is no factor that appears in each and every term. Hence, there are no common factors in this expression.

List, if any appear, the common factors in the following expressions.

no common factor

In algebra, as we now know, a letter is often used to represent some quantity. Suppose we represent some quantity by the letter *numerical coefficient* of the quantity

What does the *coefficient* of a quantity tell us?

It is important to keep in mind the difference between *coefficients* and *exponents*.

*Coefficients* record the number of like *terms* in an algebraic expression.*Exponents* record the number of like *factors* in a term.

In a term, the *coefficient* of a particular group of factors is the remaining group of factors.

how many of that quantity there are

The coefficient of

The coefficient of

The coefficient of

The coefficient of

The coefficient of

The coefficient of

Determine the coefficients.

In the term

(a)

.

(b) 6 is

.

(a) 6 (b)

In the term

(a)

.

(b)

.

(c)

.

(d)

.

(e) 3 is

.

(f) The numerical coefficient is

.

(a) 3 (b)

In the term

(a)

.

(b)

.

(c)

.

(d) 10 is

.

(e)

.

(a) 10 (b)

What is an algebraic expression?

An algebraic expression is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation.

Why is the number 14 considered to be an expression?

Why is the number

For the expressions in the following problems, write the number of terms that appear and then list the terms.

2

61

For the following problems, list, if any should appear, the common factors in the expressions.

no commom factors

For the following problems, note how many:

12

6

10

8

For the following problems, a term will be given followed by a group of its factors. List the coefficient of the given group of factors.

7

*((Reference))* Simplify

*((Reference))* Supply the missing phrase. Absolute value speaks to the question of

and not "which way."

*((Reference))* Find the value of

*((Reference))* Find the value of

*((Reference))* Express

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