Answer :
Sure, let's go through each part step by step:
### Identifying Coefficients and Degrees:
1. Term [tex]\( 3x^9 \)[/tex]
- The coefficient is [tex]\( 3 \)[/tex].
- The degree is the exponent of [tex]\( x \)[/tex], which is [tex]\( 9 \)[/tex].
2. Term [tex]\( 7x^7 \)[/tex]
- The coefficient is [tex]\( 7 \)[/tex].
- The degree is [tex]\( 7 \)[/tex].
3. Term [tex]\( -3x^3 \)[/tex]
- The coefficient is [tex]\( -3 \)[/tex].
- The degree is [tex]\( 3 \)[/tex].
4. Constant Term [tex]\( 2 \)[/tex]
- The coefficient is [tex]\( 2 \)[/tex].
- The degree of a constant term is [tex]\( 0 \)[/tex].
### Compilation and Results:
Now, let’s list the coefficients and the degrees of each term:
- For [tex]\( 3x^9 \)[/tex]:
- Coefficient: [tex]\( 3 \)[/tex]
- Degree: [tex]\( 9 \)[/tex]
- For [tex]\( 7x^7 \)[/tex]:
- Coefficient: [tex]\( 7 \)[/tex]
- Degree: [tex]\( 7 \)[/tex]
- For [tex]\( -3x^3 \)[/tex]:
- Coefficient: [tex]\( -3 \)[/tex]
- Degree: [tex]\( 3 \)[/tex]
- For the constant [tex]\( 2 \)[/tex]:
- Coefficient: [tex]\( 2 \)[/tex]
- Degree: [tex]\( 0 \)[/tex]
### Finding the Degree of the Polynomial:
The degree of a polynomial is the highest degree of its terms. So, let's list the degrees we have:
- [tex]\( 9 \)[/tex]
- [tex]\( 7 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 0 \)[/tex]
Among these, the highest degree is [tex]\( 9 \)[/tex].
### Summary:
- The coefficients for the polynomial are: [tex]\( [3, 7, -3, 2] \)[/tex]
- The degrees for the polynomial terms are: [tex]\( [9, 7, 3, 0] \)[/tex]
- The degree of the polynomial [tex]\( 3x^9 + 7x^7 - 3x^3 + 2 \)[/tex] is [tex]\( 9 \)[/tex].
So, the final answer is:
- The degree of the polynomial [tex]\( 3x^9 + 7x^7 - 3x^3 + 2 \)[/tex] is [tex]\( 9 \)[/tex].
### Identifying Coefficients and Degrees:
1. Term [tex]\( 3x^9 \)[/tex]
- The coefficient is [tex]\( 3 \)[/tex].
- The degree is the exponent of [tex]\( x \)[/tex], which is [tex]\( 9 \)[/tex].
2. Term [tex]\( 7x^7 \)[/tex]
- The coefficient is [tex]\( 7 \)[/tex].
- The degree is [tex]\( 7 \)[/tex].
3. Term [tex]\( -3x^3 \)[/tex]
- The coefficient is [tex]\( -3 \)[/tex].
- The degree is [tex]\( 3 \)[/tex].
4. Constant Term [tex]\( 2 \)[/tex]
- The coefficient is [tex]\( 2 \)[/tex].
- The degree of a constant term is [tex]\( 0 \)[/tex].
### Compilation and Results:
Now, let’s list the coefficients and the degrees of each term:
- For [tex]\( 3x^9 \)[/tex]:
- Coefficient: [tex]\( 3 \)[/tex]
- Degree: [tex]\( 9 \)[/tex]
- For [tex]\( 7x^7 \)[/tex]:
- Coefficient: [tex]\( 7 \)[/tex]
- Degree: [tex]\( 7 \)[/tex]
- For [tex]\( -3x^3 \)[/tex]:
- Coefficient: [tex]\( -3 \)[/tex]
- Degree: [tex]\( 3 \)[/tex]
- For the constant [tex]\( 2 \)[/tex]:
- Coefficient: [tex]\( 2 \)[/tex]
- Degree: [tex]\( 0 \)[/tex]
### Finding the Degree of the Polynomial:
The degree of a polynomial is the highest degree of its terms. So, let's list the degrees we have:
- [tex]\( 9 \)[/tex]
- [tex]\( 7 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( 0 \)[/tex]
Among these, the highest degree is [tex]\( 9 \)[/tex].
### Summary:
- The coefficients for the polynomial are: [tex]\( [3, 7, -3, 2] \)[/tex]
- The degrees for the polynomial terms are: [tex]\( [9, 7, 3, 0] \)[/tex]
- The degree of the polynomial [tex]\( 3x^9 + 7x^7 - 3x^3 + 2 \)[/tex] is [tex]\( 9 \)[/tex].
So, the final answer is:
- The degree of the polynomial [tex]\( 3x^9 + 7x^7 - 3x^3 + 2 \)[/tex] is [tex]\( 9 \)[/tex].
