Here’s how you can classify the given polynomials:

1. 5x²

   • Classification: Monomial
   • Reason: It has only one term.

2. 10

   • Classification: Monomial
   • Reason: It has only one term.

3. y − 1

   • Classification: Binomial
   • Reason: It has two terms.

4. 2x² − x + 3

   • Classification: Trinomial
   • Reason: It has three terms.

5. 13z + 10

   • Classification: Binomial
   • Reason: It has two terms.

6. x³ + x² − x + 1

   • Classification: Multinomial (also called Polynomial)
   • Reason: It has four terms.

7. y²

   • Classification: Monomial
   • Reason: It has only one term.

8. −4

   • Classification: Monomial
   • Reason: It has only one term.

9. 2y² − 3y + 5

   • Classification: Trinomial
   • Reason: It has three terms.

10. 3y³ + y²

• Classification: Binomial
• Reason: It has two terms.

Would you like more details or have any questions about these classifications?

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Here are 5 related questions to expand your understanding:

1. What are the key differences between monomials, binomials, and trinomials?
2. How can you determine the degree of a polynomial?
3. Why is a polynomial with more than three terms called a multinomial?
4. Can a constant term be considered a monomial? Why or why not?
5. How would you classify the polynomial $3x^2y + 4xy - 7$?

Tip: Always count the number of terms in a polynomial to classify it correctly. Terms are separated by addition (+) or subtraction (-) signs.