Select The Correct Answer.Which Term Has A Degree Of $8$?A. $-2x 3y 5$ B. $ 8 X Y 8xy 8 X Y [/tex] C. $9xy^8$ D. $3x 2y 4$

Introduction

When it comes to polynomials, understanding the concept of degree is crucial. The degree of a polynomial is a measure of its complexity, and it plays a significant role in various mathematical operations. In this article, we will delve into the world of polynomial degrees and explore how to determine the correct answer when given a polynomial with a specific degree.

What is a Polynomial Degree?

A polynomial degree is the highest power or exponent of the variable in a polynomial expression. For example, in the polynomial expression $3x^2y4$, the degree is 5, which is the sum of the exponents of x and y (2 + 4 = 5). The degree of a polynomial is denoted by the letter 'n' and is an essential concept in algebra.

Determining the Degree of a Polynomial

To determine the degree of a polynomial, we need to identify the term with the highest power or exponent of the variable. This term is called the leading term. The degree of the polynomial is then equal to the exponent of the leading term.

Example 1: Identifying the Leading Term

Consider the polynomial expression $-2x^3y5$. To determine the degree of this polynomial, we need to identify the leading term, which is $-2x^3y5$. The exponent of the leading term is 8, which is the sum of the exponents of x and y (3 + 5 = 8). Therefore, the degree of the polynomial $-2x^3y5$ is 8.

Example 2: Identifying the Leading Term

Consider the polynomial expression $8xy$. To determine the degree of this polynomial, we need to identify the leading term, which is $8xy$. The exponent of the leading term is 1, which is the sum of the exponents of x and y (1 + 0 = 1). Therefore, the degree of the polynomial $8xy$ is 1.

Example 3: Identifying the Leading Term

Consider the polynomial expression $9xy^8$. To determine the degree of this polynomial, we need to identify the leading term, which is $9xy^8$. The exponent of the leading term is 8, which is the sum of the exponents of x and y (1 + 8 = 9). However, the degree of the polynomial is determined by the highest power of the variable, which is 8. Therefore, the degree of the polynomial $9xy^8$ is 8.

Example 4: Identifying the Leading Term

Consider the polynomial expression $3x^2y4$. To determine the degree of this polynomial, we need to identify the leading term, which is $3x^2y4$. The exponent of the leading term is 6, which is the sum of the exponents of x and y (2 + 4 = 6). Therefore, the degree of the polynomial $3x^2y4$ is 6.

Conclusion

In conclusion, determining the degree of a polynomial is a crucial concept in algebra. By identifying the leading term and its exponent, we can determine the degree of the polynomial. In this article, we have explored the concept of polynomial degrees and provided examples to illustrate how to determine the correct answer when given a polynomial with a specific degree.

Final Answer

Based on the examples provided, the correct answer is:

• A. $-2x^3y5$ has a degree of 8.
• B. $8xy$ has a degree of 1.
• C. $9xy^8$ has a degree of 8.
• D. $3x^2y4$ has a degree of 6.

Therefore, the correct answer is A. $-2x^3y5$ and C. $9xy^8$, both of which have a degree of 8.

Introduction

In our previous article, we explored the concept of polynomial degrees and provided examples to illustrate how to determine the correct answer when given a polynomial with a specific degree. In this article, we will continue to delve into the world of polynomial degrees and provide a comprehensive Q&A guide to help you better understand this concept.

Q1: What is the degree of a polynomial?

A1: The degree of a polynomial is the highest power or exponent of the variable in a polynomial expression. For example, in the polynomial expression $3x^2y4$, the degree is 6, which is the sum of the exponents of x and y (2 + 4 = 6).

Q2: How do I determine the degree of a polynomial?

A2: To determine the degree of a polynomial, you need to identify the term with the highest power or exponent of the variable. This term is called the leading term. The degree of the polynomial is then equal to the exponent of the leading term.

Q3: What is the leading term of a polynomial?

A3: The leading term of a polynomial is the term with the highest power or exponent of the variable. For example, in the polynomial expression $-2x^3y5$, the leading term is $-2x^3y5$.

Q4: How do I identify the leading term of a polynomial?

A4: To identify the leading term of a polynomial, you need to look for the term with the highest power or exponent of the variable. You can do this by comparing the exponents of the variables in each term.

Q5: What is the degree of a polynomial with multiple variables?

A5: The degree of a polynomial with multiple variables is the sum of the exponents of each variable. For example, in the polynomial expression $3x^2y4z^3$, the degree is 9, which is the sum of the exponents of x, y, and z (2 + 4 + 3 = 9).

Q6: Can a polynomial have a degree of zero?

A6: Yes, a polynomial can have a degree of zero. This occurs when the polynomial has no variables or when the exponent of each variable is zero. For example, the polynomial expression $3$ has a degree of zero.

Q7: Can a polynomial have a negative degree?

A7: No, a polynomial cannot have a negative degree. The degree of a polynomial is always a non-negative integer.

Q8: How do I determine the degree of a polynomial with a negative exponent?

A8: To determine the degree of a polynomial with a negative exponent, you need to change the sign of the exponent and then determine the degree of the resulting polynomial. For example, in the polynomial expression $\frac{1}{x^2}$, the degree is -2, which is the negative of the exponent of x.

Q9: Can a polynomial have a degree of one?

A9: Yes, a polynomial can have a degree of one. This occurs when the polynomial has only one term with a variable and the exponent of the variable is one. For example, the polynomial expression $3x$ has a degree of one.

Q10: Can a polynomial have a degree of two?

A10: Yes, a polynomial can have a degree of two. This occurs when the polynomial has two terms with variables and the exponents of the variables are two. For example, the polynomial expression $3x^2y2$ has a degree of two.

Conclusion

In conclusion, determining the degree of a polynomial is a crucial concept in algebra. By understanding the concept of polynomial degrees and being able to identify the leading term, you can determine the degree of a polynomial with ease. We hope that this Q&A guide has helped you better understand this concept and has provided you with the tools you need to succeed in your mathematical endeavors.

Final Answer

Based on the Q&A guide provided, we hope that you have a better understanding of polynomial degrees and are able to determine the degree of a polynomial with ease. Remember, the degree of a polynomial is the highest power or exponent of the variable in a polynomial expression, and it is determined by the leading term.