Complete the table by naming the parts of the algebraic expression below: 

ퟑ풙 

ퟐ 

+ ퟓ풚 − 풛 + ퟐ 

Coefficients 

Variables 

Constant 

Number of Terms 

Terms 

Let's break down the given algebraic expression \( 3x^2 + 5y - z + 2 \) and fill in the table as requested:

| **Category**     | **Answer**               |
|------------------|--------------------------|
| **Coefficients** | \( 3, 5, -1 \)           |
| **Variables**    | \( x, y, z \)            |
| **Constant**     | \( 2 \)                  |
| **Number of Terms** | \( 4 \)                |
| **Terms**        | \( 3x^2, 5y, -z, 2 \)    |

**Explanation:**
1. **Coefficients**: The coefficients are the numerical factors of the variable terms: \( 3 \) (for \( x^2 \)), \( 5 \) (for \( y \)), and implicitly \( -1 \) (for \( z \)).
2. **Variables**: The variables in the expression are \( x \), \( y \), and \( z \).
3. **Constant**: The constant term is the number without a variable, which is \( 2 \).
4. **Number of Terms**: The expression consists of 4 terms: \( 3x^2 \), \( 5y \), \( -z \), and \( 2 \).
5. **Terms**: The individual components of the expression are \( 3x^2, 5y, -z, \) and \( 2 \).

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Here are some related questions:
1. What is the difference between a coefficient and a constant?
2. How do you identify the number of terms in an algebraic expression?
3. What is the significance of negative signs in terms?
4. How can we add or subtract algebraic expressions with similar terms?
5. What role do powers of variables play in algebraic terms?

**Tip:** Always pay attention to the signs of terms in an algebraic expression, as they indicate whether to add or subtract them during simplification!

Complete the table by naming the parts of the algebraic expression below: 3x^2 + 5y - z + 2

Coefficients
Variables
Constant
Number of Terms
Terms

Learn how to analyze the algebraic expression 3x^2 + 5y - z + 2 by identifying coefficients, variables, constants, and terms. This explanation is suitable for students in Grades 6-8 and covers essential algebraic concepts.

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