Training Camp (cont 14)

Look at the questions in Examples 8 and 9. What does mean in these questions? This notation is read as n is an element of the integers . Why would the question use integers when factorials are defined for only natural numbers? You must consider all values the algebraic expressions could be. This does not mean the expression includes all integers. You must define what values of n can be used.

Consider the algebraic expression from Example 9, , .

The numbers represented by n + 2 and n - 1 must both be natural numbers.

Mathematically, you represent this as follows.

When defining values of n that can be used for the algebraic expression , you must consider both n ≥ -2 and n ≥ 1. Although the integers 0, -1, and -2 are in n ≥ -2, they do not fit the restriction n ≥ 1. This means 0, -1, and -2 are not acceptable values for . When working with the expression , only values that fit n ≥ 1, are allowed.

 

 

An expression includes numbers, variables, and symbols. An equation contains expressions that are separated by an equal sign . In Example 10, you will learn how to solve algebraic equations containing factorials. To solve these equations, you need to factor trinomials. This type of factoring is reviewed in Highlights on the next page.