Classifying Polynomials worksheet with 13 algebraic expressions to classify 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) \( 5x + 1 \)
- Degree: The highest power of \( x \) is 1 (from \( 5x \)).
- Number of Terms: There are 2 terms (\( 5x \) and \( 1 \)).
- Classification: Linear binomial.

#### 2) \( 9x^2 + 3x - 1 \)
- Degree: The highest power of \( x \) is 2 (from \( 9x^2 \)).
- Number of Terms: There are 3 terms (\( 9x^2 \), \( 3x \), and \( -1 \)).
- Classification: Quadratic trinomial.

#### 3) \( -2 \)
- Degree: This is a constant polynomial, so the degree is 0.
- Number of Terms: There is 1 term (\( -2 \)).
- Classification: Constant monomial.

#### 4) \( 8x \)
- Degree: The highest power of \( x \) is 1 (from \( 8x \)).
- Number of Terms: There is 1 term (\( 8x \)).
- Classification: Linear monomial.

#### 5) \( -12x^4 + 4x^3 - 2x^2 + x \)
- Degree: The highest power of \( x \) is 4 (from \( -12x^4 \)).
- Number of Terms: There are 4 terms (\( -12x^4 \), \( 4x^3 \), \( -2x^2 \), and \( x \)).
- Classification: Quartic polynomial with 4 terms.

#### 6) \( -6 \)
- Degree: This is a constant polynomial, so the degree is 0.
- Number of Terms: There is 1 term (\( -6 \)).
- Classification: Constant monomial.

#### 7) \( -5x^6 + 2x^5 - 2x^4 \)
- Degree: The highest power of \( x \) is 6 (from \( -5x^6 \)).
- Number of Terms: There are 3 terms (\( -5x^6 \), \( 2x^5 \), and \( -2x^4 \)).
- Classification: Sextic trinomial.

#### 8) \( -2x + 3 \)
- Degree: The highest power of \( x \) is 1 (from \( -2x \)).
- Number of Terms: There are 2 terms (\( -2x \) and \( 3 \)).
- Classification: Linear binomial.

#### 9) \( -1x \)
- Degree: The highest power of \( x \) is 1 (from \( -1x \)).
- Number of Terms: There is 1 term (\( -1x \)).
- Classification: Linear monomial.

#### 10) \( -2x^2 - 3x \)
- Degree: The highest power of \( x \) is 2 (from \( -2x^2 \)).
- Number of Terms: There are 2 terms (\( -2x^2 \) and \( -3x \)).
- Classification: Quadratic binomial.

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

#### 12) \( 7x + 7 \)
- Degree: The highest power of \( x \) is 1 (from \( 7x \)).
- Number of Terms: There are 2 terms (\( 7x \) and \( 7 \)).
- Classification: Linear binomial.

#### 13) \( 9x \)
- Degree: The highest power of \( x \) is 1 (from \( 9x \)).
- Number of Terms: There is 1 term (\( 9x \)).
- Classification: Linear monomial.

Final Answer:

\[
\boxed{
\begin{array}{ll}
1) & \text{Linear binomial} \\
2) & \text{Quadratic trinomial} \\
3) & \text{Constant monomial} \\
4) & \text{Linear monomial} \\
5) & \text{Quartic polynomial with 4 terms} \\
6) & \text{Constant monomial} \\
7) & \text{Sextic trinomial} \\
8) & \text{Linear binomial} \\
9) & \text{Linear monomial} \\
10) & \text{Quadratic binomial} \\
11) & \text{Quadratic trinomial} \\
12) & \text{Linear binomial} \\
13) & \text{Linear monomial} \\
\end{array}
}
\]