The Degree Of The Polynomial $10x^2 + 2x^m Y - 4y$ Is 3. What Is The Value Of $m$?A. 1 B. 2 C. 3 D. 4

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Introduction

In mathematics, the degree of a polynomial is a fundamental concept that helps us understand the properties and behavior of polynomial functions. A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this article, we will explore the concept of the degree of a polynomial and use it to find the value of m in the given polynomial.

What is the Degree of a Polynomial?

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^2 + 2x + 1, the highest power of x is 2, so the degree of the polynomial is 2. Similarly, in the polynomial 2x^3 - 3x^2 + x - 1, the highest power of x is 3, so the degree of the polynomial is 3.

The Degree of the Given Polynomial

The given polynomial is 10x^2 + 2x^m y - 4y. To find the degree of this polynomial, we need to identify the highest power of the variable. In this case, the variable is x and y. The highest power of x is 2, and the highest power of y is m. Since the degree of the polynomial is 3, we can set up the following equation:

2 = m

Why is the Degree of the Polynomial 3?

The degree of the polynomial is 3 because the highest power of the variable is 3. In this case, the variable is x, and the highest power of x is 2. However, the polynomial also contains the term 2x^m y, which has a power of m. Since the degree of the polynomial is 3, we know that m must be equal to 1.

Solving for m

To solve for m, we can set up the following equation:

2 = m

This equation states that the highest power of the variable is 2, which is equal to m. Therefore, we can conclude that m is equal to 1.

Conclusion

In conclusion, the degree of the polynomial 10x^2 + 2x^m y - 4y is 3. To find the value of m, we need to identify the highest power of the variable. In this case, the variable is x and y, and the highest power of x is 2. However, the polynomial also contains the term 2x^m y, which has a power of m. Since the degree of the polynomial is 3, we know that m must be equal to 1.

Final Answer

The final answer is A. 1.

References

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Discussion

Introduction

In our previous article, we explored the concept of the degree of a polynomial and used it to find the value of m in the given polynomial. In this article, we will answer some frequently asked questions about the degree of a polynomial.

Q: What is the degree of a polynomial?

A: The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^2 + 2x + 1, the highest power of x is 2, so the degree of the polynomial is 2.

Q: How do you find the degree of a polynomial?

A: To find the degree of a polynomial, you need to identify the highest power of the variable in the polynomial. You can do this by looking at the terms of the polynomial and identifying the term with the highest power of the variable.

Q: What is the difference between the degree of a polynomial and the order of a polynomial?

A: The degree of a polynomial is the highest power of the variable in the polynomial, while the order of a polynomial is the number of terms in the polynomial. For example, in the polynomial 3x^2 + 2x + 1, the degree is 2 and the order is 3.

Q: Can a polynomial have a degree of 0?

A: Yes, a polynomial can have a degree of 0. For example, the polynomial 1 is a polynomial of degree 0.

Q: Can a polynomial have a degree of -1?

A: No, a polynomial cannot have a degree of -1. The degree of a polynomial is always a non-negative integer.

Q: How do you determine the degree of a polynomial with multiple variables?

A: To determine the degree of a polynomial with multiple variables, you need to identify the highest power of any of the variables in the polynomial. For example, in the polynomial 3x^2y + 2x^3z, the highest power of any of the variables is 3, so the degree of the polynomial is 3.

Q: Can a polynomial have a degree that is not a positive integer?

A: No, a polynomial cannot have a degree that is not a positive integer. The degree of a polynomial is always a non-negative integer.

Q: How do you find the value of m in a polynomial like 10x^2 + 2x^m y - 4y?

A: To find the value of m in a polynomial like 10x^2 + 2x^m y - 4y, you need to identify the highest power of the variable in the polynomial. In this case, the highest power of x is 2, and the highest power of y is m. Since the degree of the polynomial is 3, you can set up the following equation:

2 = m

This equation states that the highest power of the variable is 2, which is equal to m. Therefore, you can conclude that m is equal to 1.

Conclusion

In conclusion, the degree of a polynomial is a fundamental concept in mathematics that helps us understand the properties and behavior of polynomial functions. We hope that this Q&A article has helped you understand the degree of a polynomial and how to find the value of m in a polynomial.

Final Answer

The final answer is A. 1.

References

Additional Resources

Discussion

What is the degree of a polynomial? How do you find the degree of a polynomial? What is the value of m in a polynomial like 10x^2 + 2x^m y - 4y? Share your thoughts and questions in the comments below!