Classifying Polynomials worksheet with 15 algebraic expressions to name by degree and number of terms.

To solve the problem of classifying each polynomial by its degree and number of terms, we need to follow these steps:

Definitions:

1. Degree of a Polynomial: The highest power of the variable in the polynomial.
2. Number of Terms: The number of individual monomials (terms) in the polynomial.

Step-by-Step Solution:

#### 1) \( 5x + 8 \)
- Degree: The highest power of \( x \) is 1 (from \( 5x \)).
- Number of Terms: There are 2 terms (\( 5x \) and \( 8 \)).
- Classification: Degree 1, 2 terms.

#### 2) \( 2x^2 \)
- Degree: The highest power of \( x \) is 2.
- Number of Terms: There is 1 term (\( 2x^2 \)).
- Classification: Degree 2, 1 term.

#### 3) \( 4x^2 - 4 \)
- Degree: The highest power of \( x \) is 2 (from \( 4x^2 \)).
- Number of Terms: There are 2 terms (\( 4x^2 \) and \( -4 \)).
- Classification: Degree 2, 2 terms.

#### 4) \( 12x^4 + 2x^2 \)
- Degree: The highest power of \( x \) is 4 (from \( 12x^4 \)).
- Number of Terms: There are 2 terms (\( 12x^4 \) and \( 2x^2 \)).
- Classification: Degree 4, 2 terms.

#### 5) \( 16 \)
- Degree: Since there is no variable \( x \), the degree is 0 (constant).
- Number of Terms: There is 1 term (\( 16 \)).
- Classification: Degree 0, 1 term.

#### 6) \( 75x^4 - x^5 \)
- Degree: The highest power of \( x \) is 5 (from \( -x^5 \)).
- Number of Terms: There are 2 terms (\( 75x^4 \) and \( -x^5 \)).
- Classification: Degree 5, 2 terms.

#### 7) \( 12x^5 + 14x^3 \)
- Degree: The highest power of \( x \) is 5 (from \( 12x^5 \)).
- Number of Terms: There are 2 terms (\( 12x^5 \) and \( 14x^3 \)).
- Classification: Degree 5, 2 terms.

#### 8) \( 3x^2 + 4x - 5x^3 \)
- Degree: The highest power of \( x \) is 3 (from \( -5x^3 \)).
- Number of Terms: There are 3 terms (\( 3x^2 \), \( 4x \), and \( -5x^3 \)).
- Classification: Degree 3, 3 terms.

#### 9) \( 2x^2 + x^3 - 4 \)
- Degree: The highest power of \( x \) is 3 (from \( x^3 \)).
- Number of Terms: There are 3 terms (\( 2x^2 \), \( x^3 \), and \( -4 \)).
- Classification: Degree 3, 3 terms.

#### 10) \( 10 - x^2 \)
- Degree: The highest power of \( x \) is 2 (from \( -x^2 \)).
- Number of Terms: There are 2 terms (\( 10 \) and \( -x^2 \)).
- Classification: Degree 2, 2 terms.

#### 11) \( x^4 + 2x^3 + x^2 \)
- Degree: The highest power of \( x \) is 4 (from \( x^4 \)).
- Number of Terms: There are 3 terms (\( x^4 \), \( 2x^3 \), and \( x^2 \)).
- Classification: Degree 4, 3 terms.

#### 12) \( x + 10x^2 \)
- Degree: The highest power of \( x \) is 2 (from \( 10x^2 \)).
- Number of Terms: There are 2 terms (\( x \) and \( 10x^2 \)).
- Classification: Degree 2, 2 terms.

#### 13) \( x^5 + 3x^2 \)
- Degree: The highest power of \( x \) is 5 (from \( x^5 \)).
- Number of Terms: There are 2 terms (\( x^5 \) and \( 3x^2 \)).
- Classification: Degree 5, 2 terms.

#### 14) \( -10x^2 \)
- Degree: The highest power of \( x \) is 2.
- Number of Terms: There is 1 term (\( -10x^2 \)).
- Classification: Degree 2, 1 term.

#### 15) \( 8x^6 + 12x - 2x^4 \)
- Degree: The highest power of \( x \) is 6 (from \( 8x^6 \)).
- Number of Terms: There are 3 terms (\( 8x^6 \), \( 12x \), and \( -2x^4 \)).
- Classification: Degree 6, 3 terms.

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & \text{Degree 1, 2 terms} \\
2) & \text{Degree 2, 1 term} \\
3) & \text{Degree 2, 2 terms} \\
4) & \text{Degree 4, 2 terms} \\
5) & \text{Degree 0, 1 term} \\
6) & \text{Degree 5, 2 terms} \\
7) & \text{Degree 5, 2 terms} \\
8) & \text{Degree 3, 3 terms} \\
9) & \text{Degree 3, 3 terms} \\
10) & \text{Degree 2, 2 terms} \\
11) & \text{Degree 4, 3 terms} \\
12) & \text{Degree 2, 2 terms} \\
13) & \text{Degree 5, 2 terms} \\
14) & \text{Degree 2, 1 term} \\
15) & \text{Degree 6, 3 terms} \\
\end{array}
}
\]