College

Which of the following are terms in the expression [tex]$5r - 4s - 2$[/tex]? Select all that apply.

A. [tex]4s[/tex]
B. [tex]-4s[/tex]
C. [tex]5r - 4s[/tex]
D. [tex]-5r[/tex]
E. [tex]5[/tex]
F. [tex]-2[/tex]

Answer :

To determine the terms in the expression [tex]\(5r - 4s - 2\)[/tex], we need to identify the individual components of the expression that are separated by plus or minus signs.

Here’s a step-by-step breakdown:

1. Identify the structure of the expression:
- The expression is [tex]\(5r - 4s - 2\)[/tex].

2. Break down the expression into individual terms:
- Terms are components of an expression that are added or subtracted.
- In this expression, it is helpful to think of it as [tex]\((+5r) + (-4s) + (-2)\)[/tex], since subtraction can be seen as adding a negative.

3. List the terms:
- First term: [tex]\(5r\)[/tex]
- Second term: [tex]\(-4s\)[/tex]
- Third term: [tex]\(-2\)[/tex]

From this breakdown, we identify the terms in the expression as:

- [tex]\(5r\)[/tex]
- [tex]\(-4s\)[/tex]
- [tex]\(-2\)[/tex]

Now, let's match these terms with the options provided:

- A. [tex]\(4s\)[/tex]: This is not a term in the expression because it has a positive sign whereas our term has a negative sign.
- B. [tex]\(-4s\)[/tex]: This is a term in the expression.
- C. [tex]\(5r - 4s\)[/tex]: This is not a term; it is part of the expression but not an individual term.
- D. [tex]\(-5r\)[/tex]: This is not a term in the expression; the term is [tex]\(5r\)[/tex] without a negative sign.
- E. [tex]\(5\)[/tex]: This is not a term; it is part of the term [tex]\(5r\)[/tex].
- F. [tex]\(-2\)[/tex]: This is a term in the expression.

Therefore, the terms in the expression [tex]\(5r - 4s - 2\)[/tex] are [tex]\(-4s\)[/tex] and [tex]\(-2\)[/tex]. Select options B and F.