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what is the classification, coefficient (in order) and the degree

Let's analyze each polynomial in the table to determine its classification, coefficients (in order), and degree.

1. **Polynomial: \( 2x^2 - 3x + 20 \)**
   - **Classification:** Quadratic (since the highest exponent is 2)
   - **Coefficients (in order):** 2, -3, 20
   - **Degree:** 2

2. **Polynomial: \( x^4 - 11x + 7 \)**
   - **Classification:** Quartic (since the highest exponent is 4)
   - **Coefficients (in order):** 1, 0, 0, -11, 7
   - **Degree:** 4

3. **Polynomial: \( -2x^3 + 4x^2 - x - 3 \)**
   - **Classification:** Cubic (since the highest exponent is 3)
   - **Coefficients (in order):** -2, 4, -1, -3
   - **Degree:** 3

4. **Polynomial: \( 3x^5 + x^2 - 2 \)**
   - **Classification:** Quintic (since the highest exponent is 5)
   - **Coefficients (in order):** 3, 0, 1, 0, 0, -2
   - **Degree:** 5

5. **Polynomial: \( 1000x \)**
   - **Classification:** Linear (since the highest exponent is 1)
   - **Coefficients (in order):** 1000
   - **Degree:** 1

6. **Polynomial: \( x^4 + 2x^3 + 5x^2 + x + 1 \)**
   - **Classification:** Quartic (since the highest exponent is 4)
   - **Coefficients (in order):** 1, 2, 5, 1, 1
   - **Degree:** 4

7. **Polynomial: \( x^2 - x^7 - 2 \)**
   - **Classification:** Septic (since the highest exponent is 7)
   - **Coefficients (in order):** -1, 0, 0, 0, 0, 0, 1, -2
   - **Degree:** 7

8. **Polynomial: \( x^3 + 2x^2 - 3 \)**
   - **Classification:** Cubic (since the highest exponent is 3)
   - **Coefficients (in order):** 1, 2, 0, -3
   - **Degree:** 3

9. **Polynomial: \( 2x - 5 \)**
   - **Classification:** Linear (since the highest exponent is 1)
   - **Coefficients (in order):** 2, -5
   - **Degree:** 1

10. **Polynomial: \( \sqrt{x} - \frac{7}{x^2} \)**
    - **Classification:** Not a polynomial (due to the fractional exponent and negative exponent)
    - **Coefficients (in order):** N/A
    - **Degree:** N/A

Would you like any further details or explanations?

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**Relative Questions:**

1. What distinguishes a quadratic polynomial from a cubic polynomial?
2. Why is the polynomial \(\sqrt{x} - \frac{7}{x^2}\) not considered a true polynomial?
3. How do you determine the coefficients of a polynomial when some terms are missing (like in \(x^4 - 11x + 7\))?
4. What makes a polynomial "linear"?
5. How does the degree of a polynomial influence its graph's shape?

**Tip:** When listing coefficients, always include zeros for the missing powers of \(x\).

Explore the classification, coefficients (in order), and degrees of various polynomials such as quadratic, cubic, quartic, and more. Learn how to identify and analyze polynomials with detailed examples and explanations.

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