Identify The Degree Of Each Of The Following Polynomials And Explain How You Determined Your Answer.4. $3x^2 - 4x + 2$5. $2x^6 + 6x^4 - 15x^2 + 32$6. $x 2y 2 - 4xy + 8$7. 5 X 3 − 4 X 2 Y + 9 X Y 2 + Y + 24 5x^3 - 4x^2y + 9xy^2 + Y + 24 5 X 3 − 4 X 2 Y + 9 X Y 2 + Y + 24

In mathematics, a polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The degree of a polynomial is the highest power or exponent of the variable in the polynomial. In this article, we will identify the degree of each of the given polynomials and explain how we determined our answer.

Degree of a Polynomial

The degree of a polynomial is determined by the highest power of the variable in the polynomial. For example, in the polynomial $3x^2 - 4x + 2$, the highest power of the variable $x$ is 2. Therefore, the degree of the polynomial $3x^2 - 4x + 2$ is 2.

Determining the Degree of Each Polynomial

4. $3x^2 - 4x + 2$

To determine the degree of the polynomial $3x^2 - 4x + 2$, we need to identify the highest power of the variable $x$. In this polynomial, the highest power of the variable $x$ is 2. Therefore, the degree of the polynomial $3x^2 - 4x + 2$ is 2.

The polynomial $3x^2 - 4x + 2$ can be written as:

$$3x^2 - 4x + 2 = 3x^2 + (-4)x + 2$$

In this polynomial, the term with the highest power of the variable $x$ is $3x^2$. Therefore, the degree of the polynomial $3x^2 - 4x + 2$ is 2.

5. $2x^6 + 6x^4 - 15x^2 + 32$

To determine the degree of the polynomial $2x^6 + 6x^4 - 15x^2 + 32$, we need to identify the highest power of the variable $x$. In this polynomial, the highest power of the variable $x$ is 6. Therefore, the degree of the polynomial $2x^6 + 6x^4 - 15x^2 + 32$ is 6.

The polynomial $2x^6 + 6x^4 - 15x^2 + 32$ can be written as:

$$2x^6 + 6x^4 - 15x^2 + 32 = 2x^6 + 6x^4 + (-15)x^2 + 32$$

In this polynomial, the term with the highest power of the variable $x$ is $2x^6$. Therefore, the degree of the polynomial $2x^6 + 6x^4 - 15x^2 + 32$ is 6.

6. $x^2y^2 - 4xy + 8$

To determine the degree of the polynomial $x^2y^2 - 4xy + 8$, we need to identify the highest power of the variable $x$ and the variable $y$. In this polynomial, the highest power of the variable $x$ is 2 and the highest power of the variable $y$ is 2. Therefore, the degree of the polynomial $x^2y^2 - 4xy + 8$ is 4.

The polynomial $x^2y^2 - 4xy + 8$ can be written as:

$$x^2y^2 - 4xy + 8 = x^2y^2 + (-4)xy + 8$$

In this polynomial, the term with the highest power of the variable $x$ and the variable $y$ is $x^2y^2$. Therefore, the degree of the polynomial $x^2y^2 - 4xy + 8$ is 4.

7. $5x^3 - 4x^2y + 9xy^2 + y + 24$

To determine the degree of the polynomial $5x^3 - 4x^2y + 9xy^2 + y + 24$, we need to identify the highest power of the variable $x$ and the variable $y$. In this polynomial, the highest power of the variable $x$ is 3 and the highest power of the variable $y$ is 2. Therefore, the degree of the polynomial $5x^3 - 4x^2y + 9xy^2 + y + 24$ is 3.

The polynomial $5x^3 - 4x^2y + 9xy^2 + y + 24$ can be written as:

$$5x^3 - 4x^2y + 9xy^2 + y + 24 = 5x^3 + (-4)x^2y + 9xy^2 + y + 24$$

In this polynomial, the term with the highest power of the variable $x$ is $5x^3$. Therefore, the degree of the polynomial $5x^3 - 4x^2y + 9xy^2 + y + 24$ is 3.

Conclusion

In this article, we identified the degree of each of the given polynomials and explained how we determined our answer. The degree of a polynomial is the highest power of the variable in the polynomial. We used this definition to determine the degree of each polynomial and found that the degree of the polynomial $3x^2 - 4x + 2$ is 2, the degree of the polynomial $2x^6 + 6x^4 - 15x^2 + 32$ is 6, the degree of the polynomial $x^2y^2 - 4xy + 8$ is 4, and the degree of the polynomial $5x^3 - 4x^2y + 9xy^2 + y + 24$ is 3.

References

• [1] "Polynomial" by Wikipedia. Retrieved 2023-02-20.
• [2] "Degree of a Polynomial" by Math Open Reference. Retrieved 2023-02-20.

Keywords

• polynomial
• degree
• variable
• coefficient
• exponent
• power
• highest power
• polynomial degree
• polynomial variable
• polynomial coefficient
• polynomial exponent
• polynomial power
  Frequently Asked Questions (FAQs) About Polynomials and Their Degrees ====================================================================

In this article, we will answer some frequently asked questions about polynomials and their degrees. We will cover topics such as how to determine the degree of a polynomial, how to identify the highest power of a variable, and how to simplify polynomials.

Q: What is a polynomial?

A: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.

Q: What is the degree of a polynomial?

A: The degree of a polynomial is the highest power or exponent of the variable in the polynomial.

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

A: To determine 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 highest power of a variable?

A: The highest power of a variable is the largest exponent of the variable in the polynomial.

Q: How do I simplify a polynomial?

A: To simplify a polynomial, you need to combine like terms. Like terms are terms that have the same variable and exponent.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms.

Q: What is the coefficient of a term?

A: The coefficient of a term is the number that is multiplied by the variable in the term.

Q: How do I 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 each variable in the polynomial. The degree of the polynomial is the sum of the highest powers of the variables.

Q: What is the degree of a polynomial with variables and constants?

A: The degree of a polynomial with variables and constants is the highest power of the variable in the polynomial.

Q: Can a polynomial have a negative degree?

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

Q: Can a polynomial have a fractional degree?

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

Q: Can a polynomial have a degree of zero?

A: Yes, a polynomial can have a degree of zero. A polynomial with a degree of zero is a constant polynomial.

Q: What is a constant polynomial?

A: A constant polynomial is a polynomial with a degree of zero. It is a polynomial that has no variable and only a constant term.

Q: Can a polynomial have a degree of one?

A: Yes, a polynomial can have a degree of one. A polynomial with a degree of one is a linear polynomial.

Q: What is a linear polynomial?

A: A linear polynomial is a polynomial with a degree of one. It is a polynomial that has only one term with a variable.

Q: Can a polynomial have a degree of two?

A: Yes, a polynomial can have a degree of two. A polynomial with a degree of two is a quadratic polynomial.

Q: What is a quadratic polynomial?

A: A quadratic polynomial is a polynomial with a degree of two. It is a polynomial that has only two terms with variables.

Q: Can a polynomial have a degree of three or more?

A: Yes, a polynomial can have a degree of three or more. A polynomial with a degree of three or more is a polynomial with three or more terms with variables.

Conclusion

In this article, we answered some frequently asked questions about polynomials and their degrees. We covered topics such as how to determine the degree of a polynomial, how to identify the highest power of a variable, and how to simplify polynomials. We hope that this article has been helpful in understanding polynomials and their degrees.

References

• [1] "Polynomial" by Wikipedia. Retrieved 2023-02-20.
• [2] "Degree of a Polynomial" by Math Open Reference. Retrieved 2023-02-20.

Keywords

• polynomial
• degree
• variable
• coefficient
• exponent
• power
• highest power
• polynomial degree
• polynomial variable
• polynomial coefficient
• polynomial exponent
• polynomial power
• like terms
• combine like terms
• simplify polynomial
• constant polynomial
• linear polynomial
• quadratic polynomial