Select The Best Answer For The Question.16. Which Of The Following Is A Monomial?A. 2 X Y Z 2xy Z 2 X Yz B. 2 X Y Z 2 2xyz^2 2 X Y Z 2 C. 2 + X Y Z 2 + Xyz 2 + X Yz D. 2 X + Y Z 2x + Yz 2 X + Yz

In algebra, a monomial is an expression consisting of only one term, which can be a number, a variable, or a product of numbers and variables. It is a fundamental concept in mathematics, and understanding monomials is crucial for solving equations and manipulating algebraic expressions.

What is a Monomial?

A monomial is a single term that can be written in the form of $ax^n$, where $a$ is a constant (a number) and $n$ is a non-negative integer. The constant $a$ can be zero, but the exponent $n$ must be a non-negative integer. For example, $2x^3$, $5y^2$, and $3z$ are all monomials.

Examples of Monomials

• $2x^3$
• $5y^2$
• $3z$
• $4xy^2$
• $2x^2y^3$

Identifying Monomials

To identify a monomial, we need to check if the expression consists of only one term. If it does, then it is a monomial. For example, $2x + 3y$ is not a monomial because it consists of two terms. However, $2x$ is a monomial because it consists of only one term.

Selecting the Best Answer

Now, let's go back to the question: Which of the following is a monomial?

A. $2xy z$ B. $2xyz^2$ C. $2 + xyz$ D. $2x + yz$

To select the best answer, we need to analyze each option carefully.

• Option A: $2xy z$ consists of three terms, so it is not a monomial.
• Option B: $2xyz^2$ consists of only one term, so it is a monomial.
• Option C: $2 + xyz$ consists of two terms, so it is not a monomial.
• Option D: $2x + yz$ consists of two terms, so it is not a monomial.

Conclusion

Based on our analysis, the correct answer is B. $2xyz^2$. This is a monomial because it consists of only one term.

Key Takeaways

• A monomial is an expression consisting of only one term.
• A monomial can be written in the form of $ax^n$, where $a$ is a constant and $n$ is a non-negative integer.
• To identify a monomial, we need to check if the expression consists of only one term.
• The correct answer is B. $2xyz^2$.

Practice Problems

1. Which of the following is a monomial?
   • $2x^2 + 3y$
   • $2x^2$
   • $2x^2 + 3y^2$
   • $2x^2 + 3y^2 + 4z$
2. Which of the following is a monomial?
   • $2x + 3y$
   • $2x$
   • $2x + 3y^2$
   • $2x + 3y^2 + 4z$
3. Which of the following is a monomial?
   • $2x^2y^3$
   • $2x^2y^3 + 3z$
   • $2x^2y^3 + 3z^2$
   • $2x^2y^3 + 3z^2 + 4w$

Answer Key

1. B. $2x^2$
2. B. $2x$
3. A. $2x^2y^3$
   Frequently Asked Questions (FAQs) About Monomials =====================================================

In this article, we will answer some of the most frequently asked questions about monomials. Whether you are a student, a teacher, or simply someone who wants to learn more about algebra, this article is for you.

Q: What is a monomial?

A: A monomial is an expression consisting of only one term, which can be a number, a variable, or a product of numbers and variables.

Q: What are some examples of monomials?

A: Some examples of monomials include:

• $2x^3$
• $5y^2$
• $3z$
• $4xy^2$
• $2x^2y^3$

Q: How do I identify a monomial?

A: To identify a monomial, you need to check if the expression consists of only one term. If it does, then it is a monomial.

Q: What is the difference between a monomial and a polynomial?

A: A monomial is an expression consisting of only one term, while a polynomial is an expression consisting of two or more terms.

Q: Can a monomial have a variable with a negative exponent?

A: No, a monomial cannot have a variable with a negative exponent. The exponent of a variable in a monomial must be a non-negative integer.

Q: Can a monomial have a coefficient of zero?

A: Yes, a monomial can have a coefficient of zero. For example, $0x^2$ is a monomial.

Q: Can a monomial have more than one variable?

A: Yes, a monomial can have more than one variable. For example, $2xy^2$ is a monomial.

Q: Can a monomial have a variable with a fractional exponent?

A: No, a monomial cannot have a variable with a fractional exponent. The exponent of a variable in a monomial must be a non-negative integer.

Q: Can a monomial have a coefficient that is a fraction?

A: Yes, a monomial can have a coefficient that is a fraction. For example, $\frac{1}{2}x^2$ is a monomial.

Q: Can a monomial have a variable with a negative sign?

A: Yes, a monomial can have a variable with a negative sign. For example, $-2x^2$ is a monomial.

Q: Can a monomial have a coefficient that is a decimal number?

A: Yes, a monomial can have a coefficient that is a decimal number. For example, $3.5x^2$ is a monomial.

Q: Can a monomial have a variable with a zero exponent?

A: Yes, a monomial can have a variable with a zero exponent. For example, $2x^0$ is a monomial.

Conclusion

In this article, we have answered some of the most frequently asked questions about monomials. We have covered topics such as the definition of a monomial, examples of monomials, how to identify a monomial, and more. We hope that this article has been helpful in clarifying any confusion you may have had about monomials.

Practice Problems

1. Which of the following is a monomial?
   • $2x^2 + 3y$
   • $2x^2$
   • $2x^2 + 3y^2$
   • $2x^2 + 3y^2 + 4z$
2. Which of the following is a monomial?
   • $2x + 3y$
   • $2x$
   • $2x + 3y^2$
   • $2x + 3y^2 + 4z$
3. Which of the following is a monomial?
   • $2x^2y^3$
   • $2x^2y^3 + 3z$
   • $2x^2y^3 + 3z^2$
   • $2x^2y^3 + 3z^2 + 4w$

Answer Key

1. B. $2x^2$
2. B. $2x$
3. A. $2x^2y^3$