Identify The Degree Of This Polynomial: $-11x^3 + 10x$A. 1 B. 2 C. 3 D. 4

Introduction

In algebra, polynomials are expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The degree of a polynomial is a crucial concept in mathematics, as it determines the highest power of the variable in the polynomial. In this article, we will delve into the world of polynomials and explore how to identify the degree of a 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 $2x^3 + 3x^2 - 4x + 1$, the highest power of the variable $x$ is 3. Therefore, the degree of this polynomial is 3.

Identifying the Degree of a Polynomial: A Step-by-Step Guide

To identify the degree of a polynomial, follow these steps:

1. Write down the polynomial: Start by writing down the given polynomial.
2. Identify the terms: Identify the individual terms in the polynomial. A term is a single variable or a product of variables and coefficients.
3. Determine the power of each term: Determine the power of each term in the polynomial. The power of a term is the exponent of the variable.
4. Find the highest power: Find the highest power of the variable in the polynomial. This is the degree of the polynomial.

Example 1: Identifying the Degree of a Polynomial

Let's consider the polynomial $-11x^3 + 10x$. To identify the degree of this polynomial, follow the steps outlined above.

1. Write down the polynomial: The given polynomial is $-11x^3 + 10x$.
2. Identify the terms: The individual terms in the polynomial are $-11x^3$ and $10x$.
3. Determine the power of each term: The power of the term $-11x^3$ is 3, and the power of the term $10x$ is 1.
4. Find the highest power: The highest power of the variable $x$ in the polynomial is 3.

Therefore, the degree of the polynomial $-11x^3 + 10x$ is 3.

Example 2: Identifying the Degree of a Polynomial with Multiple Terms

Let's consider the polynomial $2x^3 + 3x^2 - 4x + 1$. To identify the degree of this polynomial, follow the steps outlined above.

1. Write down the polynomial: The given polynomial is $2x^3 + 3x^2 - 4x + 1$.
2. Identify the terms: The individual terms in the polynomial are $2x^3$, $3x^2$, $-4x$, and $1$.
3. Determine the power of each term: The power of the term $2x^3$ is 3, the power of the term $3x^2$ is 2, the power of the term $-4x$ is 1, and the power of the term $1$ is 0.
4. Find the highest power: The highest power of the variable $x$ in the polynomial is 3.

Therefore, the degree of the polynomial $2x^3 + 3x^2 - 4x + 1$ is 3.

Conclusion

In conclusion, identifying the degree of a polynomial is a straightforward process that involves writing down the polynomial, identifying the terms, determining the power of each term, and finding the highest power. By following these steps, you can easily identify the degree of a given polynomial.

Final Answer

The final answer to the problem is:

The degree of the polynomial $-11x^3 + 10x$ is 3.

References

• [1] Khan Academy. (n.d.). Polynomials. Retrieved from https://www.khanacademy.org/math/algebra/x2f4f7d1/x2f4f7d1-polynomials
• [2] Math Open Reference. (n.d.). Polynomials. Retrieved from https://www.mathopenref.com/poly.html

Additional Resources

• [1] Algebra.com. (n.d.). Polynomials. Retrieved from https://www.algebra.com/algebra/homework/polynomials/polynomials.html
• [2] Purplemath. (n.d.). Polynomials. Retrieved from https://www.purplemath.com/modules/polydefs.htm
  Frequently Asked Questions: Identifying 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 $2x^3 + 3x^2 - 4x + 1$, the highest power of the variable $x$ is 3. Therefore, the degree of this polynomial is 3.

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

A: To identify the degree of a polynomial, follow these steps:

1. Write down the polynomial: Start by writing down the given polynomial.
2. Identify the terms: Identify the individual terms in the polynomial. A term is a single variable or a product of variables and coefficients.
3. Determine the power of each term: Determine the power of each term in the polynomial. The power of a term is the exponent of the variable.
4. Find the highest power: Find the highest power of the variable in the polynomial. This is the degree of the polynomial.

Q: What if the polynomial has multiple terms with the same power?

A: If the polynomial has multiple terms with the same power, the degree of the polynomial is still the highest power of the variable. For example, in the polynomial $2x^3 + 3x^3 - 4x + 1$, the highest power of the variable $x$ is 3. Therefore, the degree of this polynomial is 3.

Q: What if the polynomial has a term with a negative exponent?

A: If the polynomial has a term with a negative exponent, the degree of the polynomial is still the highest power of the variable. For example, in the polynomial $2x^3 + 3x^2 - 4x^{-1} + 1$, the highest power of the variable $x$ is 3. Therefore, the degree of this polynomial is 3.

Q: Can a polynomial have a degree of 0?

A: Yes, a polynomial can have a degree of 0. A polynomial with a degree of 0 is a constant polynomial, which is a polynomial with no variable. For example, the polynomial $1$ has a degree of 0.

Q: Can a polynomial have a degree of 1?

A: Yes, a polynomial can have a degree of 1. A polynomial with a degree of 1 is a linear polynomial, which is a polynomial with one variable and a power of 1. For example, the polynomial $2x + 3$ has a degree of 1.

Q: Can a polynomial have a degree of 2?

A: Yes, a polynomial can have a degree of 2. A polynomial with a degree of 2 is a quadratic polynomial, which is a polynomial with one variable and a power of 2. For example, the polynomial $2x^2 + 3x + 1$ has a degree of 2.

Q: Can a polynomial have a degree of 3?

A: Yes, a polynomial can have a degree of 3. A polynomial with a degree of 3 is a cubic polynomial, which is a polynomial with one variable and a power of 3. For example, the polynomial $2x^3 + 3x^2 - 4x + 1$ has a degree of 3.

Q: Can a polynomial have a degree greater than 3?

A: Yes, a polynomial can have a degree greater than 3. For example, the polynomial $2x^4 + 3x^3 - 4x^2 + x + 1$ has a degree of 4.

Conclusion

In conclusion, identifying the degree of a polynomial is a straightforward process that involves writing down the polynomial, identifying the terms, determining the power of each term, and finding the highest power. By following these steps, you can easily identify the degree of a given polynomial.

Final Answer

The final answer to the problem is:

• The degree of a polynomial is the highest power of the variable in the polynomial.
• To identify the degree of a polynomial, follow the steps outlined above.
• A polynomial can have a degree of 0, 1, 2, 3, or any other positive integer.

References

• [1] Khan Academy. (n.d.). Polynomials. Retrieved from https://www.khanacademy.org/math/algebra/x2f4f7d1/x2f4f7d1-polynomials
• [2] Math Open Reference. (n.d.). Polynomials. Retrieved from https://www.mathopenref.com/poly.html

Additional Resources

• [1] Algebra.com. (n.d.). Polynomials. Retrieved from https://www.algebra.com/algebra/homework/polynomials/polynomials.html
• [2] Purplemath. (n.d.). Polynomials. Retrieved from https://www.purplemath.com/modules/polydefs.htm