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Copy and complete the table below (in ½ crosswise yellow paper)
Polynomial
Classification
Coefficients (in 
order)
Degree

I can help you complete the table based on the provided polynomials. Here's the breakdown:

### 1. Polynomial: \(2x^3 - 5x^2 + 20\)
   - **Classification**: Cubic (since the highest power is 3)
   - **Coefficients (in order)**: \(2, -5, 0, 20\) (since there is no \(x\) term, its coefficient is 0)
   - **Degree**: 3

### 2. Polynomial: \(4x^2 - 11x - 7\)
   - **Classification**: Quadratic (since the highest power is 2)
   - **Coefficients (in order)**: \(4, -11, -7\)
   - **Degree**: 2

### 3. Polynomial: \(x^4 + 3x^2 - 2\)
   - **Classification**: Quartic (since the highest power is 4)
   - **Coefficients (in order)**: \(1, 0, 3, 0, -2\) (coefficients of \(x^3\) and \(x\) are 0)
   - **Degree**: 4

### 4. Polynomial: \(x^2 + 1\)
   - **Classification**: Quadratic (since the highest power is 2)
   - **Coefficients (in order)**: \(1, 0, 1\) (since there is no \(x\) term, its coefficient is 0)
   - **Degree**: 2

### 5. Polynomial: \(1000x\)
   - **Classification**: Linear (since the highest power is 1)
   - **Coefficients (in order)**: \(1000, 0\)
   - **Degree**: 1

### 6. Polynomial: \(4x^4\)
   - **Classification**: Quartic (since the highest power is 4)
   - **Coefficients (in order)**: \(4, 0, 0, 0, 0\)
   - **Degree**: 4

### 7. Polynomial: \(3x^3 - x\)
   - **Classification**: Cubic (since the highest power is 3)
   - **Coefficients (in order)**: \(3, 0, -1, 0\)
   - **Degree**: 3

### 8. Polynomial: \(x^2 - x^2 = 0\)
   - **Classification**: Zero polynomial (since it simplifies to 0)
   - **Coefficients (in order)**: \(0\)
   - **Degree**: Undefined (commonly set to \(-\infty\))

### 9. Polynomial: \(x + \frac{1}{x}\)
   - **Classification**: Not a polynomial (since the term \(\frac{1}{x}\) is not allowed in a polynomial)
   - **Coefficients (in order)**: Undefined
   - **Degree**: Undefined

### 10. Polynomial: \(\sqrt{x} + \frac{1}{x}\)
   - **Classification**: Not a polynomial (since the term \(\sqrt{x}\) and \(\frac{1}{x}\) are not allowed in a polynomial)
   - **Coefficients (in order)**: Undefined
   - **Degree**: Undefined

Would you like any further details or explanations on any of these polynomials?

Here are five related questions:
1. What distinguishes a polynomial from a non-polynomial expression?
2. How do you determine the degree of a polynomial?
3. Why is the classification of a polynomial important in algebra?
4. What happens to the classification when a polynomial is reduced to a constant?
5. How do fractional and radical expressions affect polynomial classification?

**Tip:** Always check for missing degrees in polynomials, especially when coefficients are zero, to ensure the polynomial is classified correctly.

Learn how to classify polynomials and determine coefficients with examples. Understand polynomial degrees and classifications including cubic, quadratic, and linear polynomials. Suitable for high school students studying algebra and polynomial functions.

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