Certainly! Let's analyze each polynomial to understand how the number of terms is determined.
### Polynomial Analysis
#### Polynomial 1: [tex]\( 5x \)[/tex]
The expression [tex]\( 5x \)[/tex] is a single term by itself. There are no additional terms added or subtracted in this polynomial.
- Number of Terms: 1
#### Polynomial 2: [tex]\( 2x^2 + 5x + 2 \)[/tex]
This polynomial consists of three distinct terms:
1. [tex]\( 2x^2 \)[/tex]
2. [tex]\( 5x \)[/tex]
3. [tex]\( 2 \)[/tex]
Each term is separated by a plus (+) sign.
- Number of Terms: 3
#### Polynomial 3: [tex]\( x^2 - 1 \)[/tex]
This polynomial has two distinct terms:
1. [tex]\( x^2 \)[/tex]
2. [tex]\( -1 \)[/tex]
Each term is separated by a minus (-) sign.
- Number of Terms: 2
### Summary Table
Let's summarize our findings in a table:
| Polynomial | Number of Terms |
|---------------------|-----------------|
| [tex]\( 5x \)[/tex] | 1 |
| [tex]\( 2x^2 + 5x + 2 \)[/tex] | 3 |
| [tex]\( x^2 - 1 \)[/tex] | 2 |
### Conclusion
From this analysis, we can conclude that the number of terms in a polynomial is determined by the distinct parts of the polynomial expression that are separated by addition (+) or subtraction (-) signs. Each separate part is considered a term.
The number of terms for the given polynomials is:
- Polynomial [tex]\( 5x \)[/tex]: 1 term
- Polynomial [tex]\( 2x^2 + 5x + 2 \)[/tex]: 3 terms
- Polynomial [tex]\( x^2 - 1 \)[/tex]: 2 terms
