Pick the expression that matches this description:
A monomial of the 
\[2^{\text{nd}}\] degree with a leading coefficient of 
\[3\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   
\[2n^3\]
A
\[2n^3\]
(Choice B)   
\[3n^2\]
B
\[3n^2\]
(Choice C)   
\[3n^2-1\]
C
\[3n^2-1\]
(Choice D)   
\[3n-n^2\]
D
\[3n-n^2\]

To find a monomial of the 2nd degree with a leading coefficient of 3, let's analyze the choices:

- **Choice A**: \(2n^3\)
  - This is a monomial, but it is of the 3rd degree, not the 2nd.

- **Choice B**: \(3n^2\)
  - This is a monomial of the 2nd degree (the exponent is 2) and has a leading coefficient of 3.

- **Choice C**: \(3n^2 - 1\)
  - This is a polynomial (specifically a binomial), not a monomial.

- **Choice D**: \(3n - n^2\)
  - This is a polynomial (specifically a binomial) and the term with the highest degree is \(-n^2\), which means it is not a monomial of the 2nd degree with a leading coefficient of 3.

Given these analyses, the correct answer is:

- (B) \(3n^2\)

**Would you like more details or have any questions about monomials and their properties?**

Here are 8 related questions for further exploration:

1. What defines a monomial and how does it differ from other types of polynomials?
2. Can a monomial have more than one variable? If yes, give an example.
3. What is the degree of the monomial \(4x^3y^2\)?
4. How do you determine the leading coefficient of a polynomial?
5. Why is \(3n^2\) considered a monomial and \(3n^2 - 1\) not?
6. How do you add and subtract monomials?
7. What happens when you multiply two monomials?
8. Can the degree of a monomial be negative or a fraction? Why or why not?

**Tip**: A monomial is a single term consisting of a coefficient and variables raised to non-negative integer powers. Always ensure that the degree matches the requirements specified in the problem.

Learn how to identify a monomial of the 2nd degree with a leading coefficient of 3. This problem explores properties of monomials and polynomials, emphasizing understanding of degrees and coefficients. Suitable for Grades 7-9 students.

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