Identify the parts of each algebraic expressions by completing the table. 

a. −푏푐 

2 

+2푑+9    

Coefficients 

Variables 

Constant 

Terms 

Classify 

b. 3푥 

2 

+4푦 

3 

−푧+11 

Coefficients 

Variables 

Constant 

Terms 

Classify 

Let's analyze the two algebraic expressions and break them down according to the requested categories.

### Expression a:  
\[
-\frac{bc}{2} + 2d + 9
\]

| **Category**  | **Expression a** |
|---------------|------------------|
| **Coefficients** | -1/2 (for \(bc\)), 2 (for \(d\)) |
| **Variables**    | \(b\), \(c\), \(d\) |
| **Constant**     | 9 |
| **Terms**        | \(-\frac{bc}{2}\), \(2d\), 9 |
| **Classify**     | Trinomial (since there are three terms) |

### Expression b:  
\[
3x^2 + 4y^3 - z + 11
\]

| **Category**  | **Expression b** |
|---------------|------------------|
| **Coefficients** | 3 (for \(x^2\)), 4 (for \(y^3\)), -1 (for \(z\)) |
| **Variables**    | \(x\), \(y\), \(z\) |
| **Constant**     | 11 |
| **Terms**        | \(3x^2\), \(4y^3\), \(-z\), 11 |
| **Classify**     | Polynomial with four terms (also known as a quadrinomial) |

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Do you need further clarification on any part of this analysis?

Here are 5 related questions for deeper understanding:

1. How do you identify a coefficient in an algebraic expression?
2. What is the difference between a monomial, binomial, and trinomial?
3. Can an algebraic expression have no constants?
4. How do you classify expressions with more than three terms?
5. How does the degree of a term differ from the number of terms in an expression?

**Tip:** In algebraic expressions, the degree of a term is the sum of the exponents of the variables in that term.

Identify the parts of each algebraic expression by completing the table.

a. −푏푐/2 + 2푑 + 9
Coefficients
Variables
Constant
Terms
Classify

b. 3푥^2 + 4푦^3 − z + 11
Coefficients
Variables
Constant
Terms
Classify

Learn how to identify the terms, coefficients, variables, and constants of algebraic expressions such as −bc/2 + 2d + 9 and 3x^2 + 4y^3 − z + 11. This problem helps students classify polynomials and break down complex expressions into simpler components. Suitable for students in Grades 7-10.

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