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The problem is asking us to analyze the function \( f(x) = 2x + x^5 \) to determine if it is a polynomial function. If it is, we should state its degree, identify the leading term, the constant term, and write it in standard form.

### Solution

1. **Determine if it’s a polynomial function**:  
   A polynomial function is an expression that consists of terms in the form \( ax^n \), where \( a \) is a coefficient and \( n \) is a non-negative integer. The function \( f(x) = 2x + x^5 \) meets these criteria since it has terms \( 2x \) and \( x^5 \) (both with non-negative integer exponents).

2. **Standard Form**:  
   The standard form of a polynomial arranges terms in descending order of their powers. Thus, we rewrite \( f(x) = x^5 + 2x \).

3. **Degree of the Polynomial**:  
   The degree of a polynomial is the highest power of \( x \). In this case, the highest power is \( 5 \), so the degree of this polynomial is \( 5 \).

4. **Leading Term**:  
   The leading term is the term with the highest degree, which is \( x^5 \).

5. **Constant Term**:  
   A constant term is a term with no variable attached. Since there is no constant term in \( f(x) = x^5 + 2x \), the constant term is \( 0 \).

### Summary
- **Polynomial Function**: Yes
- **Standard Form**: \( f(x) = x^5 + 2x \)
- **Degree**: 5
- **Leading Term**: \( x^5 \)
- **Constant Term**: \( 0 \)

Would you like further details or have any questions?

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Here are some related questions to explore:
1. How do we determine if a function is a polynomial?
2. What are examples of non-polynomial functions?
3. How do we find the degree of a polynomial with multiple terms?
4. Why is the highest power term called the "leading term"?
5. How does the constant term affect the polynomial function graph?

**Tip**: When writing polynomials in standard form, always order terms by descending powers of \( x \) for clarity.

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree. If it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term. f(x) = 2x + x^5

Learn how to analyze the function f(x) = 2x + x^5 to determine if it’s a polynomial function. Understand its degree, identify the leading term and constant term, and rewrite it in standard form. Ideal for students in Grades 10-12.

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