Certainly! Let's carefully analyze the given polynomial and identify its characteristics step by step.
### Given Polynomial:
[tex]\[ 8a^5 - 6a^3 \][/tex]
1. Determining the Degree of the Polynomial:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- In the given polynomial, the terms are [tex]\( 8a^5 \)[/tex] and [tex]\( -6a^3 \)[/tex].
- The powers of the variable [tex]\( a \)[/tex] in these terms are 5 and 3, respectively.
- The highest power is 5.
- Therefore, the degree of the polynomial is 5.
2. Counting the Number of Terms:
- A term in a polynomial is any product of numbers and variables separated by addition (+) or subtraction (-) signs.
- In the polynomial [tex]\( 8a^5 - 6a^3 \)[/tex], we have two distinct terms: [tex]\( 8a^5 \)[/tex] and [tex]\( -6a^3 \)[/tex].
- Thus, the number of terms in the polynomial is 2.
3. Naming the Polynomial:
- A polynomial can be named by combining its degree and the number of terms it contains.
- Since the polynomial has a degree of 5 and consists of 2 terms, we use the following terminology:
- Degree: 5 → "5th degree"
- Number of terms: 2 → "Binomial" (since 'bi-' indicates two terms)
Therefore, the correct name for the polynomial [tex]\( 8a^5 - 6a^3 \)[/tex] is:
[tex]\[ \text{5th degree Binomial} \][/tex]
### Conclusion:
By classifying the given polynomial based on its degree and the number of terms, we name the polynomial as:
[tex]\[ \text{5th degree Binomial} \][/tex]
