Answer the questions about the following polynomial.
one half, plus, 5, x, to the power 4 , minus, 7, x, plus, x, squared
2
1
​
 +5x 
4
 −7x+x 
2
 
Answer
Attempt 2 out of 5

The expression represents a 
 polynomial with 
 terms. The constant term is 
, the leading term is 
, and the leading coefficient is 
.

Let's break down the expression and answer the questions step by step:

The given polynomial is:
\[
\frac{1}{2} + 5x^4 - 7x + x^2
\]

### 1. Number of Terms:
The expression contains the following terms:
- \(\frac{1}{2}\) (constant term)
- \(5x^4\) (term with degree 4)
- \(-7x\) (term with degree 1)
- \(x^2\) (term with degree 2)

Thus, there are **4 terms** in the polynomial.

### 2. Constant Term:
The constant term is the term that does not involve any variable. In this case, the constant term is:
\[
\frac{1}{2}
\]

### 3. Leading Term:
The leading term is the term with the highest degree. In this case, the term with the highest degree is:
\[
5x^4
\]

### 4. Leading Coefficient:
The leading coefficient is the coefficient of the leading term. For the term \(5x^4\), the leading coefficient is:
\[
5
\]

### Final Answers:
- The expression represents a **polynomial with 4 terms**.
- The constant term is **\(\frac{1}{2}\)**.
- The leading term is **\(5x^4\)**.
- The leading coefficient is **5**.

Let me know if you'd like further details or explanations! Also, here are some related questions to explore:

1. What is the degree of this polynomial?
2. How can we simplify polynomials with more than one variable?
3. What is the difference between a monomial and a polynomial?
4. How do we determine the end behavior of a polynomial?
5. Can we factor this polynomial? If so, how?

**Tip:** To identify the leading term of a polynomial, always look for the term with the highest exponent on the variable.

Answer the questions about the following polynomial: one half, plus, 5, x, to the power 4 , minus, 7, x, plus, x, squared

Learn how to analyze the terms, constant term, leading term, and leading coefficient of a polynomial. This example includes a polynomial with 4 terms: 5x^4, -7x, x^2, and 1/2. Ideal for students in Grades 8-10 studying polynomials.

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