Copy and complete the table below (in ½ crosswise yellow paper)
Polynomial
Classification
Coefficients (in 
order)
Degree
1 2𝑥3 − 3𝑥 + 10
2 9𝑥2 − 11𝑥 − 3
3 2 − 8𝑥 + 𝑥2 − 𝑥3
4 2𝑥3 + √5𝑥 − 2
5 1000𝑥
6 75,462
7 0
8 2𝑥3 + √5𝑥2 − 2
9 3 + 𝑥 − 5𝑥3
10 6𝑥
5
+ √2

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

---

**1. Polynomial: \( 2x^3 - 3x + 10 \)**  
- **Classification:** Cubic  
- **Coefficients (in order):** 2, 0, -3, 10  
- **Degree:** 3  

**2. Polynomial: \( 9x^2 - 11x - 3 \)**  
- **Classification:** Quadratic  
- **Coefficients (in order):** 9, -11, -3  
- **Degree:** 2  

**3. Polynomial: \( 2 - 8x + x^2 - x^3 \)**  
- **Classification:** Cubic  
- **Coefficients (in order):** -1, 1, -8, 2  
- **Degree:** 3  

**4. Polynomial: \( 2x^3 + \sqrt{5}x - 2 \)**  
- **Classification:** Cubic  
- **Coefficients (in order):** 2, 0, \(\sqrt{5}\), -2  
- **Degree:** 3  

**5. Polynomial: \( 1000x \)**  
- **Classification:** Linear  
- **Coefficients (in order):** 1000  
- **Degree:** 1  

**6. Polynomial: \( 75,462 \)**  
- **Classification:** Constant  
- **Coefficients (in order):** 75,462  
- **Degree:** 0  

**7. Polynomial: \( 0 \)**  
- **Classification:** Zero polynomial (degree undefined or often considered -∞)  
- **Coefficients (in order):** 0  
- **Degree:** Undefined  

**8. Polynomial: \( 2x^3 + \sqrt{5}x^2 - 2 \)**  
- **Classification:** Cubic  
- **Coefficients (in order):** 2, \(\sqrt{5}\), 0, -2  
- **Degree:** 3  

**9. Polynomial: \( 3 + x - 5x^3 \)**  
- **Classification:** Cubic  
- **Coefficients (in order):** -5, 0, 1, 3  
- **Degree:** 3  

**10. Polynomial: \( 6x^{\frac{5}{2}} + \sqrt{2} \)**  
- **Classification:** Not a polynomial (fractional exponent)  
- **Coefficients (in order):** N/A  
- **Degree:** N/A  

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Would you like any further details or explanations?

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**Relative Questions:**

1. Why is a constant polynomial classified as having a degree of 0?
2. What is the difference between a zero polynomial and a constant polynomial?
3. Why does the presence of a fractional exponent disqualify an expression from being considered a polynomial?
4. How can you determine the degree of a polynomial when the terms are not arranged in descending order?
5. What would the classification be for a polynomial with degree 4?

**Tip:** When writing polynomials, always arrange terms in descending order of degree for clarity and easier identification of coefficients and degrees.

Explore polynomial classification and coefficients with examples. Learn about cubic, quadratic, linear, and constant polynomials, their coefficients in order, and their degrees. Suitable for students studying advanced algebra and polynomial functions in Grades 9-12.

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