Identify the variable and constant terms in the expression.​ Also, identify the coefficient of each variable term.
5 x Superscript 4 Baseline minus 2 x squared plus 9 x minus 8
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Part 1
A.
​Variable: 5x Superscript 4​, negative 2x squared​, 9x
​Constant: negative 8
Coefficient in 5x Superscript 4​: 4
Coefficient in negative 2x squared​: 2
Coefficient in 9​x: 1
B.
​Variable: 5x Superscript 4​, negative 2x squared
​Constant: 9​, negative 8
Coefficient in 5x Superscript 4​: 5
Coefficient in negative 2x squared​: negative 2
C.
​Variable: 5x Superscript 4​, negative 2x squared​, 9x
​Constant: negative 8
Coefficient in 5x Superscript 4​: 5
Coefficient in negative 2x squared​: negative 2
Coefficient in 9​x: 9
D.
​Variable: 5x Superscript 4​, negative 2x squared​, 9x
​Constant: negative 8
Coefficient in 5x Superscript 4​: x Superscript 4
Coefficient in negative 2x squared​: x squared
Coefficient in 9​x: x

Let's analyze the expression \(5x^4 - 2x^2 + 9x - 8\) in detail.

### 1. **Variable Terms:**
- The terms involving the variable \(x\) are:
  - \(5x^4\)
  - \(-2x^2\)
  - \(9x\)

### 2. **Constant Term:**
- The constant term is the number that does not contain any variables. In this case, it is:
  - \(-8\)

### 3. **Coefficients:**
- The coefficient of a variable term is the number that multiplies the variable. Now, let’s identify them:
  - In \(5x^4\), the coefficient is **5**.
  - In \(-2x^2\), the coefficient is **-2**.
  - In \(9x\), the coefficient is **9**.

### Correct Answer:
- **Variable terms**: \(5x^4\), \(-2x^2\), \(9x\)
- **Constant**: \(-8\)
- **Coefficients**:
  - Coefficient of \(5x^4\): 5
  - Coefficient of \(-2x^2\): -2
  - Coefficient of \(9x\): 9

Therefore, the correct answer is **C**:
- Variables: \(5x^4\), \(-2x^2\), \(9x\)
- Constant: \(-8\)
- Coefficients: 5, -2, 9

Would you like further clarification on this?

Here are 5 related questions to help you understand better:
1. What is a coefficient in a mathematical expression?
2. How do you identify variable terms in a polynomial?
3. What role does the constant term play in an expression?
4. Can a variable term have a negative coefficient?
5. How does the degree of a term relate to its variable?

**Tip**: Always remember that the coefficient is the numerical factor multiplying the variable in a term.

Identify the variable and constant terms in the expression. Also, identify the coefficient of each variable term: 5x^4 - 2x^2 + 9x - 8

Learn how to identify the variable and constant terms in the polynomial expression 5x^4 - 2x^2 + 9x - 8. Understand how to determine the coefficients of each variable term. This problem covers key algebraic concepts and is suitable for students in Grades 8-10.

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