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Answer :
Sure! Let's break down each part of the question step by step and find the degree of each term and the polynomial.
1. Find the degree of the term [tex]\(3x^9\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(3x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(9\)[/tex].
- Therefore, the degree of the term [tex]\(3x^9\)[/tex] is [tex]\(9\)[/tex].
2. Find the degree of the term [tex]\(-3\)[/tex]:
- A constant term (a term without a variable) has a degree of [tex]\(0\)[/tex].
- Since [tex]\(-3\)[/tex] is a constant term, its degree is [tex]\(0\)[/tex].
3. Find the degree of the term [tex]\(4x^6\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(4x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(6\)[/tex].
- Therefore, the degree of the term [tex]\(4x^6\)[/tex] is [tex]\(6\)[/tex].
4. Find the degree of the term [tex]\(2x^8\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(2x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(8\)[/tex].
- Therefore, the degree of the term [tex]\(2x^8\)[/tex] is [tex]\(8\)[/tex].
5. Find the degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex]:
- The degree of a polynomial is the highest degree of all its terms.
- The degrees of the individual terms are:
- [tex]\(3x^9\)[/tex] has degree [tex]\(9\)[/tex].
- [tex]\(-3\)[/tex] has degree [tex]\(0\)[/tex].
- [tex]\(4x^6\)[/tex] has degree [tex]\(6\)[/tex].
- [tex]\(2x^8\)[/tex] has degree [tex]\(8\)[/tex].
- The highest degree among these is [tex]\(9\)[/tex].
- Therefore, the degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex] is [tex]\(9\)[/tex].
In summary:
- The degree of the term [tex]\(3x^9\)[/tex] is [tex]\(9\)[/tex].
- The degree of the term [tex]\(-3\)[/tex] is [tex]\(0\)[/tex].
- The degree of the term [tex]\(4x^6\)[/tex] is [tex]\(6\)[/tex].
- The degree of the term [tex]\(2x^8\)[/tex] is [tex]\(8\)[/tex].
- The degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex] is [tex]\(9\)[/tex].
So, the final answer is:
[tex]\[
\boxed{9}
\][/tex]
[tex]\[
\boxed{0}
\][/tex]
[tex]\[
\boxed{6}
\][/tex]
[tex]\[
\boxed{8}
\][/tex]
[tex]\[
\boxed{9}
\][/tex]
1. Find the degree of the term [tex]\(3x^9\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(3x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(9\)[/tex].
- Therefore, the degree of the term [tex]\(3x^9\)[/tex] is [tex]\(9\)[/tex].
2. Find the degree of the term [tex]\(-3\)[/tex]:
- A constant term (a term without a variable) has a degree of [tex]\(0\)[/tex].
- Since [tex]\(-3\)[/tex] is a constant term, its degree is [tex]\(0\)[/tex].
3. Find the degree of the term [tex]\(4x^6\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(4x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(6\)[/tex].
- Therefore, the degree of the term [tex]\(4x^6\)[/tex] is [tex]\(6\)[/tex].
4. Find the degree of the term [tex]\(2x^8\)[/tex]:
- The degree of a term is the exponent of the variable [tex]\(x\)[/tex].
- For the term [tex]\(2x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(8\)[/tex].
- Therefore, the degree of the term [tex]\(2x^8\)[/tex] is [tex]\(8\)[/tex].
5. Find the degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex]:
- The degree of a polynomial is the highest degree of all its terms.
- The degrees of the individual terms are:
- [tex]\(3x^9\)[/tex] has degree [tex]\(9\)[/tex].
- [tex]\(-3\)[/tex] has degree [tex]\(0\)[/tex].
- [tex]\(4x^6\)[/tex] has degree [tex]\(6\)[/tex].
- [tex]\(2x^8\)[/tex] has degree [tex]\(8\)[/tex].
- The highest degree among these is [tex]\(9\)[/tex].
- Therefore, the degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex] is [tex]\(9\)[/tex].
In summary:
- The degree of the term [tex]\(3x^9\)[/tex] is [tex]\(9\)[/tex].
- The degree of the term [tex]\(-3\)[/tex] is [tex]\(0\)[/tex].
- The degree of the term [tex]\(4x^6\)[/tex] is [tex]\(6\)[/tex].
- The degree of the term [tex]\(2x^8\)[/tex] is [tex]\(8\)[/tex].
- The degree of the polynomial [tex]\(3x^9 - 3 + 4x^6 + 2x^8\)[/tex] is [tex]\(9\)[/tex].
So, the final answer is:
[tex]\[
\boxed{9}
\][/tex]
[tex]\[
\boxed{0}
\][/tex]
[tex]\[
\boxed{6}
\][/tex]
[tex]\[
\boxed{8}
\][/tex]
[tex]\[
\boxed{9}
\][/tex]
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