Properties of Polynomials | CK-12 Foundation - Free Printable

Let's solve this step by step.

We are given a set of algebraic expressions and need to classify each as Monomial, Binomial, or Trinomial based on the number of terms in the expression.

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Definitions:

- Monomial: An expression with one term (e.g., $ 2x^3 $)
- Binomial: An expression with two terms (e.g., $ 5x + 3 $)
- Trinomial: An expression with three terms (e.g., $ 1 + 4x + 5x^2 $)

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Now, let’s examine each expression:

#### Row 1:
1. $ 1 + 4x + 5x^2 $ → Three terms → Trinomial
2. $ 5x^4 + 6x^5 $ → Two terms → Binomial
3. $ 7x + 10 $ → Two terms → Binomial

#### Row 2:
4. $ 2x^3 $ → One term → Monomial
5. $ 2x^6 + x^7 + 4x^8 $ → Three terms → Trinomial
6. $ 3x^3 + 6x^4 + 3x^5 $ → Three terms → Trinomial

#### Row 3:
7. $ 5x + 3 $ → Two terms → Binomial
8. $ 2x^2 $ → One term → Monomial
9. $ 3x^6 $ → One term → Monomial

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Now, match each expression to the correct category:

#### Monomial (One term):
- $ 2x^3 $
- $ 2x^2 $
- $ 3x^6 $

#### Binomial (Two terms):
- $ 5x^4 + 6x^5 $
- $ 7x + 10 $
- $ 5x + 3 $

#### Trinomial (Three terms):
- $ 1 + 4x + 5x^2 $
- $ 2x^6 + x^7 + 4x^8 $
- $ 3x^3 + 6x^4 + 3x^5 $

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Final Answer:

✔ Monomial:
- $ 2x^3 $
- $ 2x^2 $
- $ 3x^6 $

✔ Binomial:
- $ 5x^4 + 6x^5 $
- $ 7x + 10 $
- $ 5x + 3 $

✔ Trinomial:
- $ 1 + 4x + 5x^2 $
- $ 2x^6 + x^7 + 4x^8 $
- $ 3x^3 + 6x^4 + 3x^5 $

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You can now drag or assign each expression to its correct category in the image. The "Check" button would verify if all are correctly classified.