Types Of Polynomials Math Worksheet Worksheet - Free Printable

Problem Overview:

The task is to simplify each given polynomial expression (if possible) and then classify each polynomial as a monomial, binomial, or trinomial. Let's solve this step by step.

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Definitions:

1. Monomial: A polynomial with exactly one term.
2. Binomial: A polynomial with exactly two terms.
3. Trinomial: A polynomial with exactly three terms.

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Step-by-Step Solution:

#### 1. \( 6x + 7y \)
- Simplify: This expression cannot be simplified further because the terms \( 6x \) and \( 7y \) are not like terms.
- Classification: This has two terms, so it is a binomial.

#### 2. \( x^2 - 9x + 2 \)
- Simplify: This expression cannot be simplified further because the terms \( x^2 \), \( -9x \), and \( 2 \) are not like terms.
- Classification: This has three terms, so it is a trinomial.

#### 3. \( 8x + 5x \)
- Simplify: Combine like terms:
\[
8x + 5x = 13x
\]
- Classification: After simplification, this has one term, so it is a monomial.

#### 4. \( -7.5 \)
- Simplify: This is already in its simplest form.
- Classification: This has one term, so it is a monomial.

#### 5. \( 3 + 8m \)
- Simplify: This expression cannot be simplified further because the terms \( 3 \) and \( 8m \) are not like terms.
- Classification: This has two terms, so it is a binomial.

#### 6. \( y^2 - 7 + 9y \)
- Simplify: This expression cannot be simplified further because the terms \( y^2 \), \( 9y \), and \( -7 \) are not like terms.
- Classification: This has three terms, so it is a trinomial.

#### 7. \( 3x^2 + 8y \)
- Simplify: This expression cannot be simplified further because the terms \( 3x^2 \) and \( 8y \) are not like terms.
- Classification: This has two terms, so it is a binomial.

#### 8. \( 7y - y \)
- Simplify: Combine like terms:
\[
7y - y = 6y
\]
- Classification: After simplification, this has one term, so it is a monomial.

#### 9. \( 4x + 5x - 8 \)
- Simplify: Combine like terms:
\[
4x + 5x - 8 = 9x - 8
\]
- Classification: After simplification, this has two terms, so it is a binomial.

#### 10. \( p^2 - p^3 - 1 \)
- Simplify: This expression cannot be simplified further because the terms \( p^2 \), \( -p^3 \), and \( -1 \) are not like terms.
- Classification: This has three terms, so it is a trinomial.

#### 11. \( x^2 - 9x + 2 \)
- Simplify: This expression cannot be simplified further because the terms \( x^2 \), \( -9x \), and \( 2 \) are not like terms.
- Classification: This has three terms, so it is a trinomial.

#### 12. \( y^2 - y \)
- Simplify: This expression cannot be simplified further because the terms \( y^2 \) and \( -y \) are not like terms.
- Classification: This has two terms, so it is a binomial.

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Final Answer:

\[
\boxed{
\begin{array}{ccc}
6x + 7y & \text{Binomial} \\
x^2 - 9x + 2 & \text{Trinomial} \\
8x + 5x & \text{Monomial} \\
-7.5 & \text{Monomial} \\
3 + 8m & \text{Binomial} \\
y^2 - 7 + 9y & \text{Trinomial} \\
3x^2 + 8y & \text{Binomial} \\
7y - y & \text{Monomial} \\
4x + 5x - 8 & \text{Binomial} \\
p^2 - p^3 - 1 & \text{Trinomial} \\
x^2 - 9x + 2 & \text{Trinomial} \\
y^2 - y & \text{Binomial}
\end{array}
}
\]