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Answer :
Certainly! Let's go through each part of the question one step at a time.
1. Find the degree of the term [tex]\(-4x^8\)[/tex]:
- The degree of a term is the exponent of the variable in that term.
- Here, the term is [tex]\(-4x^8\)[/tex]. The exponent of [tex]\(x\)[/tex] is 8.
- So, the degree of the term [tex]\(-4x^8\)[/tex] is 8.
2. Find the degree of the term [tex]\(-3\)[/tex]:
- A constant term (with no variable) is considered to have a degree of 0.
- Therefore, the degree of the term [tex]\(-3\)[/tex] is 0.
3. Find the degree of the term [tex]\(-6x^6\)[/tex]:
- For the term [tex]\(-6x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6.
- Thus, the degree of the term [tex]\(-6x^6\)[/tex] is 6.
4. Find the degree of the term [tex]\(4x^9\)[/tex]:
- Here, the term is [tex]\(4x^9\)[/tex] and the exponent of [tex]\(x\)[/tex] is 9.
- So, the degree of the term [tex]\(4x^9\)[/tex] is 9.
5. Find the degree of the polynomial [tex]\(-4x^8 - 3 - 6x^6 + 4x^9\)[/tex]:
- The degree of a polynomial is determined by the term with the highest degree.
- We have the following degrees from the terms of the polynomial:
- [tex]\(-4x^8\)[/tex] has degree 8
- [tex]\(-3\)[/tex] has degree 0
- [tex]\(-6x^6\)[/tex] has degree 6
- [tex]\(4x^9\)[/tex] has degree 9
- The highest degree among these is 9.
- Therefore, the degree of the polynomial [tex]\(-4x^8 - 3 - 6x^6 + 4x^9\)[/tex] is 9.
I hope this detailed explanation helps! If you have any more questions, feel free to ask.
1. Find the degree of the term [tex]\(-4x^8\)[/tex]:
- The degree of a term is the exponent of the variable in that term.
- Here, the term is [tex]\(-4x^8\)[/tex]. The exponent of [tex]\(x\)[/tex] is 8.
- So, the degree of the term [tex]\(-4x^8\)[/tex] is 8.
2. Find the degree of the term [tex]\(-3\)[/tex]:
- A constant term (with no variable) is considered to have a degree of 0.
- Therefore, the degree of the term [tex]\(-3\)[/tex] is 0.
3. Find the degree of the term [tex]\(-6x^6\)[/tex]:
- For the term [tex]\(-6x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6.
- Thus, the degree of the term [tex]\(-6x^6\)[/tex] is 6.
4. Find the degree of the term [tex]\(4x^9\)[/tex]:
- Here, the term is [tex]\(4x^9\)[/tex] and the exponent of [tex]\(x\)[/tex] is 9.
- So, the degree of the term [tex]\(4x^9\)[/tex] is 9.
5. Find the degree of the polynomial [tex]\(-4x^8 - 3 - 6x^6 + 4x^9\)[/tex]:
- The degree of a polynomial is determined by the term with the highest degree.
- We have the following degrees from the terms of the polynomial:
- [tex]\(-4x^8\)[/tex] has degree 8
- [tex]\(-3\)[/tex] has degree 0
- [tex]\(-6x^6\)[/tex] has degree 6
- [tex]\(4x^9\)[/tex] has degree 9
- The highest degree among these is 9.
- Therefore, the degree of the polynomial [tex]\(-4x^8 - 3 - 6x^6 + 4x^9\)[/tex] is 9.
I hope this detailed explanation helps! If you have any more questions, feel free to ask.
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