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Answer :
Let's break down each part of the polynomial [tex]\(9x^7 + 6x^5 - 6x^3 + 1\)[/tex] to determine the coefficient and degree of each term, and also find the degree of the entire polynomial.
1. Term: [tex]\(9x^7\)[/tex]
- The coefficient is the numerical part of the term, which is 9.
- The degree of the term is the exponent of [tex]\(x\)[/tex], which is 7.
2. Term: [tex]\(6x^5\)[/tex]
- The coefficient is 6.
- The degree of the term is 5.
3. Term: [tex]\(-6x^3\)[/tex]
- The coefficient is [tex]\(-6\)[/tex].
- The degree of the term is 3.
4. Constant Term: [tex]\(1\)[/tex]
- The coefficient of a constant term is the constant itself, which is 1.
- The degree of a constant term is 0 because there is no [tex]\(x\)[/tex] present.
The degree of the polynomial is determined by the term with the highest degree. In this case, the highest degree is from the term [tex]\(9x^7\)[/tex], which is 7. Thus, the degree of the polynomial is 7.
In summary:
- Coefficient of [tex]\(9x^7\)[/tex]: 9
- Degree of [tex]\(9x^7\)[/tex]: 7
- Coefficient of [tex]\(6x^5\)[/tex]: 6
- Degree of [tex]\(6x^5\)[/tex]: 5
- Coefficient of [tex]\(-6x^3\)[/tex]: [tex]\(-6\)[/tex]
- Degree of [tex]\(-6x^3\)[/tex]: 3
- Coefficient of 1: 1
- Degree of 1: 0
- Degree of the polynomial: 7
1. Term: [tex]\(9x^7\)[/tex]
- The coefficient is the numerical part of the term, which is 9.
- The degree of the term is the exponent of [tex]\(x\)[/tex], which is 7.
2. Term: [tex]\(6x^5\)[/tex]
- The coefficient is 6.
- The degree of the term is 5.
3. Term: [tex]\(-6x^3\)[/tex]
- The coefficient is [tex]\(-6\)[/tex].
- The degree of the term is 3.
4. Constant Term: [tex]\(1\)[/tex]
- The coefficient of a constant term is the constant itself, which is 1.
- The degree of a constant term is 0 because there is no [tex]\(x\)[/tex] present.
The degree of the polynomial is determined by the term with the highest degree. In this case, the highest degree is from the term [tex]\(9x^7\)[/tex], which is 7. Thus, the degree of the polynomial is 7.
In summary:
- Coefficient of [tex]\(9x^7\)[/tex]: 9
- Degree of [tex]\(9x^7\)[/tex]: 7
- Coefficient of [tex]\(6x^5\)[/tex]: 6
- Degree of [tex]\(6x^5\)[/tex]: 5
- Coefficient of [tex]\(-6x^3\)[/tex]: [tex]\(-6\)[/tex]
- Degree of [tex]\(-6x^3\)[/tex]: 3
- Coefficient of 1: 1
- Degree of 1: 0
- Degree of the polynomial: 7
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