Identify the coefficient and the degree of each term of the polynomial then find the first degree of the polynomial

96x³y⁷-8x⁴yz-2

Let's break down the polynomial \( 96x^3y^7 - 8x^4yz - 2 \) into its individual terms and analyze the **coefficients** and **degrees**.

### 1. First term: \( 96x^3y^7 \)
- **Coefficient**: 96
- **Degree**: The total degree of this term is the sum of the exponents on all variables. Here, the exponent of \( x \) is 3, and the exponent of \( y \) is 7. So, the degree is:
  \[
  3 + 7 = 10
  \]

### 2. Second term: \( -8x^4yz \)
- **Coefficient**: -8
- **Degree**: The exponents are as follows: \( x^4 \), \( y^1 \) (implicit), and \( z^1 \) (implicit). So, the degree is:
  \[
  4 + 1 + 1 = 6
  \]

### 3. Third term: \( -2 \)
- **Coefficient**: -2
- **Degree**: This is a constant term (no variables). Therefore, its degree is:
  \[
  0
  \]

### Degree of the Polynomial
The **degree of a polynomial** is the highest degree among its terms. Here, the degrees of the terms are:
- \( 96x^3y^7 \) has degree 10,
- \( -8x^4yz \) has degree 6,
- \( -2 \) has degree 0.

So, the degree of the polynomial is:
\[
\boxed{10}
\]

### Coefficients Summary
- First term: Coefficient = 96, Degree = 10
- Second term: Coefficient = -8, Degree = 6
- Third term: Coefficient = -2, Degree = 0

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Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between the degree of a term and the degree of a polynomial?
2. How do you determine the degree of a constant term?
3. What role do coefficients play in polynomial functions?
4. How do you find the degree of multivariable terms like \( x^2y^3 \)?
5. Can the degree of a polynomial be negative?

**Tip**: The degree of a polynomial helps in identifying its behavior at large values of the variable(s).

Identify the coefficient and the degree of each term of the polynomial then find the first degree of the polynomial 96x³y⁷ - 8x⁴yz - 2

Analyze the polynomial 96x³y⁷ - 8x⁴yz - 2 by breaking down its terms to find the coefficients and degrees. Learn how to determine the degree of each term and find the overall degree of the polynomial. Suitable for students in Grades 9-12 studying algebra and polynomials.

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