Identifying Terms Coefficients And Constants Worksheet Answer Key ... - Free Printable

To solve the problem, we need to identify the number of terms, coefficients, and constants in each given algebraic expression. Let's go through each expression step by step.

Definitions:

- Term: A part of an expression separated by addition or subtraction.
- Coefficient: The numerical factor of a term.
- Constant: A term that does not contain any variables.

Solution:

#### 1. \( x + 1 \)
- # of Terms: 2 ( \( x \) and \( 1 \) )
- Coefficients: 1 (coefficient of \( x \))
- Constants: 1

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 1 | 2 | 1 | 1 |

#### 2. \( 2x^2 + x - 3 \)
- # of Terms: 3 ( \( 2x^2 \), \( x \), and \( -3 \) )
- Coefficients: 2 (coefficient of \( x^2 \)), 1 (coefficient of \( x \))
- Constants: -3

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 2 | 3 | 2, 1 | -3 |

#### 3. \( 4 \)
- # of Terms: 1 ( \( 4 \) )
- Coefficients: None (no variable)
- Constants: 4

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 3 | 1 | None | 4 |

#### 4. \( 10x^3yz \)
- # of Terms: 1 ( \( 10x^3yz \) )
- Coefficients: 10
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 4 | 1 | 10 | None |

#### 5. \( 3x - 6 \)
- # of Terms: 2 ( \( 3x \) and \( -6 \) )
- Coefficients: 3 (coefficient of \( x \))
- Constants: -6

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 5 | 2 | 3 | -6 |

#### 6. \( 7y^3 - 4y^2 + 2 \)
- # of Terms: 3 ( \( 7y^3 \), \( -4y^2 \), and \( 2 \) )
- Coefficients: 7 (coefficient of \( y^3 \)), -4 (coefficient of \( y^2 \))
- Constants: 2

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 6 | 3 | 7, -4 | 2 |

#### 7. \( -10 \)
- # of Terms: 1 ( \( -10 \) )
- Coefficients: None (no variable)
- Constants: -10

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 7 | 1 | None | -10 |

#### 8. \( a + 2b + 4c + d \)
- # of Terms: 4 ( \( a \), \( 2b \), \( 4c \), and \( d \) )
- Coefficients: 1 (coefficient of \( a \)), 2 (coefficient of \( b \)), 4 (coefficient of \( c \)), 1 (coefficient of \( d \))
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 8 | 4 | 1, 2, 4, 1 | None |

#### 9. \( r^2 + 11r \)
- # of Terms: 2 ( \( r^2 \) and \( 11r \) )
- Coefficients: 1 (coefficient of \( r^2 \)), 11 (coefficient of \( r \))
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 9 | 2 | 1, 11 | None |

#### 10. \( 0 \)
- # of Terms: 1 ( \( 0 \) )
- Coefficients: None (no variable)
- Constants: 0

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 10 | 1 | None | 0 |

#### 11. \( 3x^2y^4 \)
- # of Terms: 1 ( \( 3x^2y^4 \) )
- Coefficients: 3
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 11 | 1 | 3 | None |

#### 12. \( 4x^3 - 4x^2 + x + 3 \)
- # of Terms: 4 ( \( 4x^3 \), \( -4x^2 \), \( x \), and \( 3 \) )
- Coefficients: 4 (coefficient of \( x^3 \)), -4 (coefficient of \( x^2 \)), 1 (coefficient of \( x \))
- Constants: 3

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 12 | 4 | 4, -4, 1 | 3 |

#### 13. \( 2x^3 - 1 \)
- # of Terms: 2 ( \( 2x^3 \) and \( -1 \) )
- Coefficients: 2 (coefficient of \( x^3 \))
- Constants: -1

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 13 | 2 | 2 | -1 |

#### 14. \( 6y \)
- # of Terms: 1 ( \( 6y \) )
- Coefficients: 6
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 14 | 1 | 6 | None |

#### 15. \( -4x^4 \)
- # of Terms: 1 ( \( -4x^4 \) )
- Coefficients: -4
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 15 | 1 | -4 | None |

#### 16. \( 5x^4y^3 \)
- # of Terms: 1 ( \( 5x^4y^3 \) )
- Coefficients: 5
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 16 | 1 | 5 | None |

#### 17. \( x^2 + x - 3 \)
- # of Terms: 3 ( \( x^2 \), \( x \), and \( -3 \) )
- Coefficients: 1 (coefficient of \( x^2 \)), 1 (coefficient of \( x \))
- Constants: -3

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 17 | 3 | 1, 1 | -3 |

#### 18. \( -3x \)
- # of Terms: 1 ( \( -3x \) )
- Coefficients: -3
- Constants: None (all terms involve variables)

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 18 | 1 | -3 | None |

#### 19. \( 4x^2 - 1 \)
- # of Terms: 2 ( \( 4x^2 \) and \( -1 \) )
- Coefficients: 4 (coefficient of \( x^2 \))
- Constants: -1

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 19 | 2 | 4 | -1 |

#### 20. \( 7x^6 - 3x^3 + 2 \)
- # of Terms: 3 ( \( 7x^6 \), \( -3x^3 \), and \( 2 \) )
- Coefficients: 7 (coefficient of \( x^6 \)), -3 (coefficient of \( x^3 \))
- Constants: 2

| Problem # | # of Terms | Coefficients | Constants |
|-----------|------------|--------------|-----------|
| 20 | 3 | 7, -3 | 2 |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Problem \#} & \text{\# of Terms} & \text{Coefficients} & \text{Constants} \\
\hline
1 & 2 & 1 & 1 \\
2 & 3 & 2, 1 & -3 \\
3 & 1 & \text{None} & 4 \\
4 & 1 & 10 & \text{None} \\
5 & 2 & 3 & -6 \\
6 & 3 & 7, -4 & 2 \\
7 & 1 & \text{None} & -10 \\
8 & 4 & 1, 2, 4, 1 & \text{None} \\
9 & 2 & 1, 11 & \text{None} \\
10 & 1 & \text{None} & 0 \\
11 & 1 & 3 & \text{None} \\
12 & 4 & 4, -4, 1 & 3 \\
13 & 2 & 2 & -1 \\
14 & 1 & 6 & \text{None} \\
15 & 1 & -4 & \text{None} \\
16 & 1 & 5 & \text{None} \\
17 & 3 & 1, 1 & -3 \\
18 & 1 & -3 & \text{None} \\
19 & 2 & 4 & -1 \\
20 & 3 & 7, -3 & 2 \\
\hline
\end{array}
}
\]