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Answer :
Sure! Let's go through each part of the question step by step:
1. Find the degree of the term [tex]\(4x^9\)[/tex]:
- A term's degree is the exponent of the variable in that term.
- In [tex]\(4x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is 9.
- So, the degree of the term [tex]\(4x^9\)[/tex] is 9.
2. Find the degree of the term 3:
- A constant term like 3 does not have a variable attached to it.
- By convention, the degree of a constant term is 0.
- So, the degree of the term 3 is 0.
3. Find the degree of the term [tex]\(5x^8\)[/tex]:
- The degree of a term is given by the exponent of the variable.
- Here, in [tex]\(5x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is 8.
- Thus, the degree of the term [tex]\(5x^8\)[/tex] is 8.
4. Find the degree of the term [tex]\(-5x^6\)[/tex]:
- The exponent of the variable in a term determines its degree.
- In [tex]\(-5x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6.
- Therefore, the degree of the term [tex]\(-5x^6\)[/tex] is 6.
5. Find the degree of the polynomial [tex]\(4x^9 + 3 + 5x^8 - 5x^6\)[/tex]:
- To find the degree of a polynomial, look for the term with the highest degree among all its terms.
- From the degrees we found above: [tex]\(9\)[/tex] (from [tex]\(4x^9\)[/tex]), [tex]\(0\)[/tex] (from 3), [tex]\(8\)[/tex] (from [tex]\(5x^8\)[/tex]), and [tex]\(6\)[/tex] (from [tex]\(-5x^6\)[/tex]).
- The highest degree is 9.
- Therefore, the degree of the polynomial is 9.
I hope this helps you understand how to find the degree of terms and polynomials! If you have any more questions, feel free to ask.
1. Find the degree of the term [tex]\(4x^9\)[/tex]:
- A term's degree is the exponent of the variable in that term.
- In [tex]\(4x^9\)[/tex], the exponent of [tex]\(x\)[/tex] is 9.
- So, the degree of the term [tex]\(4x^9\)[/tex] is 9.
2. Find the degree of the term 3:
- A constant term like 3 does not have a variable attached to it.
- By convention, the degree of a constant term is 0.
- So, the degree of the term 3 is 0.
3. Find the degree of the term [tex]\(5x^8\)[/tex]:
- The degree of a term is given by the exponent of the variable.
- Here, in [tex]\(5x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is 8.
- Thus, the degree of the term [tex]\(5x^8\)[/tex] is 8.
4. Find the degree of the term [tex]\(-5x^6\)[/tex]:
- The exponent of the variable in a term determines its degree.
- In [tex]\(-5x^6\)[/tex], the exponent of [tex]\(x\)[/tex] is 6.
- Therefore, the degree of the term [tex]\(-5x^6\)[/tex] is 6.
5. Find the degree of the polynomial [tex]\(4x^9 + 3 + 5x^8 - 5x^6\)[/tex]:
- To find the degree of a polynomial, look for the term with the highest degree among all its terms.
- From the degrees we found above: [tex]\(9\)[/tex] (from [tex]\(4x^9\)[/tex]), [tex]\(0\)[/tex] (from 3), [tex]\(8\)[/tex] (from [tex]\(5x^8\)[/tex]), and [tex]\(6\)[/tex] (from [tex]\(-5x^6\)[/tex]).
- The highest degree is 9.
- Therefore, the degree of the polynomial is 9.
I hope this helps you understand how to find the degree of terms and polynomials! If you have any more questions, feel free to ask.
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