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.