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Fenger in PontezOCJ

[tex]3x^9 + 7x^7 - 3x^3 + 2[/tex]

1. The coefficient of the term [tex]3x^9[/tex] is 3.
2. The degree of the term [tex]3x^9[/tex] is 9.
3. The coefficient of the term [tex]7x^7[/tex] is 7.
4. The degree of the term [tex]7x^7[/tex] is 7.
5. The coefficient of the term [tex]-3x^3[/tex] is -3.
6. The degree of the term [tex]-3x^3[/tex] is 3.
7. The coefficient of the term 2 is 2.
8. The degree of the term 2 is 0.

The degree of the polynomial [tex]3x^9 + 7x^7 - 3x^3 + 2[/tex] is [tex]\square[/tex].

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].

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