Answer :
To solve the given problem, we need to find the degree of each term in the expression and then determine the degree of the entire polynomial.
1. Find the degree of the term [tex]\(3x^9\)[/tex]:
- A term's degree is determined by the exponent of the variable. In [tex]\(3x^9\)[/tex], the variable [tex]\(x\)[/tex] has an exponent of 9.
- Degree: 9
2. Find the degree of the term [tex]\(-4\)[/tex]:
- This term is a constant. The degree of a constant is always 0 because it can be thought of as [tex]\(4x^0\)[/tex].
- Degree: 0
3. Find the degree of the term [tex]\(1x^6\)[/tex]:
- Here, the variable [tex]\(x\)[/tex] has an exponent of 6.
- Degree: 6
4. Find the degree of the term [tex]\(-6x^8\)[/tex]:
- For this term, the variable [tex]\(x\)[/tex] has an exponent of 8.
- Degree: 8
5. Find the degree of the polynomial [tex]\(3x^9 - 4 + 1x^6 - 6x^8\)[/tex]:
- The degree of a polynomial is the highest degree of its terms.
- We identified the degrees of the terms as 9, 0, 6, and 8. The highest degree among these is 9.
- Degree of the polynomial: 9
So, the degree for each term and the polynomial is as follows:
- [tex]\(3x^9\)[/tex]: 9
- [tex]\(-4\)[/tex]: 0
- [tex]\(1x^6\)[/tex]: 6
- [tex]\(-6x^8\)[/tex]: 8
- Polynomial degree: 9
1. Find the degree of the term [tex]\(3x^9\)[/tex]:
- A term's degree is determined by the exponent of the variable. In [tex]\(3x^9\)[/tex], the variable [tex]\(x\)[/tex] has an exponent of 9.
- Degree: 9
2. Find the degree of the term [tex]\(-4\)[/tex]:
- This term is a constant. The degree of a constant is always 0 because it can be thought of as [tex]\(4x^0\)[/tex].
- Degree: 0
3. Find the degree of the term [tex]\(1x^6\)[/tex]:
- Here, the variable [tex]\(x\)[/tex] has an exponent of 6.
- Degree: 6
4. Find the degree of the term [tex]\(-6x^8\)[/tex]:
- For this term, the variable [tex]\(x\)[/tex] has an exponent of 8.
- Degree: 8
5. Find the degree of the polynomial [tex]\(3x^9 - 4 + 1x^6 - 6x^8\)[/tex]:
- The degree of a polynomial is the highest degree of its terms.
- We identified the degrees of the terms as 9, 0, 6, and 8. The highest degree among these is 9.
- Degree of the polynomial: 9
So, the degree for each term and the polynomial is as follows:
- [tex]\(3x^9\)[/tex]: 9
- [tex]\(-4\)[/tex]: 0
- [tex]\(1x^6\)[/tex]: 6
- [tex]\(-6x^8\)[/tex]: 8
- Polynomial degree: 9
