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Answer :
Let's find the degree of each term and the polynomial step-by-step.
1. Degree of the term [tex]\(-2x^9\)[/tex]:
The degree of a term in a polynomial is the exponent of the variable. For [tex]\(-2x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is 9. So, the degree of this term is 9.
2. Degree of the term [tex]\(-6x^8\)[/tex]:
Similarly, in [tex]\(-6x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is 8. Therefore, the degree of this term is 8.
3. Degree of the term [tex]\(2\)[/tex]:
When we have a constant term like 2, it can be thought of as [tex]\(2x^0\)[/tex] since any number to the power of 0 is 1 and [tex]\(x^0 = 1\)[/tex]. Therefore, the degree of a constant term is 0.
4. Degree of the term [tex]\(-4x^6\)[/tex]:
In [tex]\(-4x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6. So, the degree of this term is 6.
5. Degree of the polynomial [tex]\(-2x^9 - 6x^8 + 2 - 4x^6\)[/tex]:
The degree of a polynomial is the highest degree among all its terms. Here, the degrees of the terms are 9, 8, 0, and 6. The highest of these degrees is 9.
Putting it all together:
- Degree of [tex]\(-2x^9\)[/tex] is 9.
- Degree of [tex]\(-6x^8\)[/tex] is 8.
- Degree of [tex]\(2\)[/tex] is 0.
- Degree of [tex]\(-4x^6\)[/tex] is 6.
- Degree of the polynomial is 9.
So the final answers are:
- Degree of the term [tex]\(-2x^9\)[/tex] is 9.
- Degree of the term [tex]\(-6x^8\)[/tex] is 8.
- Degree of the term 2 is 0.
- Degree of the term [tex]\(-4x^6\)[/tex] is 6.
- Degree of the polynomial [tex]\(-2x^9 - 6x^8 + 2 - 4x^6\)[/tex] is 9.
1. Degree of the term [tex]\(-2x^9\)[/tex]:
The degree of a term in a polynomial is the exponent of the variable. For [tex]\(-2x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is 9. So, the degree of this term is 9.
2. Degree of the term [tex]\(-6x^8\)[/tex]:
Similarly, in [tex]\(-6x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is 8. Therefore, the degree of this term is 8.
3. Degree of the term [tex]\(2\)[/tex]:
When we have a constant term like 2, it can be thought of as [tex]\(2x^0\)[/tex] since any number to the power of 0 is 1 and [tex]\(x^0 = 1\)[/tex]. Therefore, the degree of a constant term is 0.
4. Degree of the term [tex]\(-4x^6\)[/tex]:
In [tex]\(-4x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6. So, the degree of this term is 6.
5. Degree of the polynomial [tex]\(-2x^9 - 6x^8 + 2 - 4x^6\)[/tex]:
The degree of a polynomial is the highest degree among all its terms. Here, the degrees of the terms are 9, 8, 0, and 6. The highest of these degrees is 9.
Putting it all together:
- Degree of [tex]\(-2x^9\)[/tex] is 9.
- Degree of [tex]\(-6x^8\)[/tex] is 8.
- Degree of [tex]\(2\)[/tex] is 0.
- Degree of [tex]\(-4x^6\)[/tex] is 6.
- Degree of the polynomial is 9.
So the final answers are:
- Degree of the term [tex]\(-2x^9\)[/tex] is 9.
- Degree of the term [tex]\(-6x^8\)[/tex] is 8.
- Degree of the term 2 is 0.
- Degree of the term [tex]\(-4x^6\)[/tex] is 6.
- Degree of the polynomial [tex]\(-2x^9 - 6x^8 + 2 - 4x^6\)[/tex] is 9.
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