What Is The Additive Inverse Of The Polynomial \[$-7y^2 + X^2y - 3xy - 7x^2\$\]?A. \[$7y^2 - X^2y + 3xy + 7x^2\$\] B. \[$7y^2 + X^2y + 3xy + 7x^2\$\] C. \[$-7y^2 - X^2y - 3xy - 7x^2\$\] D. \[$7y^2 + X^2y - 3xy -

In mathematics, the additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term. In other words, it is the polynomial that, when added to the original polynomial, cancels out all the terms and leaves only the zero polynomial.

What is the Additive Inverse of a Polynomial?

The additive inverse of a polynomial is denoted by the symbol -p(x), where p(x) is the original polynomial. To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.

Finding the Additive Inverse of a Polynomial

To find the additive inverse of a polynomial, we can follow these steps:

1. Write down the original polynomial.
2. Change the sign of each term in the polynomial.
3. Simplify the resulting polynomial.

Example: Finding the Additive Inverse of a Polynomial

Let's consider the polynomial -7y^2 + x^2y - 3xy - 7x^2. To find its additive inverse, we need to change the sign of each term in the polynomial.

-7y^2 + x^2y - 3xy - 7x^2

Changing the sign of each term, we get:

7y^2 - x^2y + 3xy + 7x^2

Therefore, the additive inverse of the polynomial -7y^2 + x^2y - 3xy - 7x^2 is 7y^2 - x^2y + 3xy + 7x^2.

Answer Choice Analysis

Now, let's analyze the answer choices:

A. 7y^2 - x^2y + 3xy + 7x^2 B. 7y^2 + x^2y + 3xy + 7x^2 C. -7y^2 - x^2y - 3xy - 7x^2 D. 7y^2 + x^2y - 3xy - 7x^2

Based on our analysis, we can see that answer choice A is the correct additive inverse of the polynomial -7y^2 + x^2y - 3xy - 7x^2.

Conclusion

In conclusion, the additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term. To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial. In this article, we analyzed the answer choices and determined that the correct additive inverse of the polynomial -7y^2 + x^2y - 3xy - 7x^2 is 7y^2 - x^2y + 3xy + 7x^2.

Key Takeaways

• The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term.
• To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.
• The additive inverse of a polynomial is denoted by the symbol -p(x), where p(x) is the original polynomial.

Frequently Asked Questions

• What is the additive inverse of a polynomial?
• How do I find the additive inverse of a polynomial?
• What is the symbol used to denote the additive inverse of a polynomial?

Answer to Frequently Asked Questions

• The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term.
• To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.
• The symbol used to denote the additive inverse of a polynomial is -p(x), where p(x) is the original polynomial.
  Additive Inverse of a Polynomial: Q&A =====================================

In our previous article, we discussed the concept of the additive inverse of a polynomial and how to find it. In this article, we will answer some frequently asked questions related to the additive inverse of a polynomial.

Q: What is the additive inverse of a polynomial?

A: The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term. In other words, it is the polynomial that, when added to the original polynomial, cancels out all the terms and leaves only the zero polynomial.

Q: How do I find the additive inverse of a polynomial?

A: To find the additive inverse of a polynomial, you need to change the sign of each term in the polynomial. This means that if a term is positive, you need to change it to negative, and if a term is negative, you need to change it to positive.

Q: What is the symbol used to denote the additive inverse of a polynomial?

A: The symbol used to denote the additive inverse of a polynomial is -p(x), where p(x) is the original polynomial.

Q: Can you give an example of finding the additive inverse of a polynomial?

A: Let's consider the polynomial -7y^2 + x^2y - 3xy - 7x^2. To find its additive inverse, we need to change the sign of each term in the polynomial.

-7y^2 + x^2y - 3xy - 7x^2

Changing the sign of each term, we get:

7y^2 - x^2y + 3xy + 7x^2

Therefore, the additive inverse of the polynomial -7y^2 + x^2y - 3xy - 7x^2 is 7y^2 - x^2y + 3xy + 7x^2.

Q: What is the difference between the additive inverse and the negative of a polynomial?

A: The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term. The negative of a polynomial, on the other hand, is a polynomial that is obtained by changing the sign of each term in the polynomial. While the additive inverse and the negative of a polynomial are related, they are not the same thing.

Q: Can you give an example of a polynomial that has the same additive inverse as the original polynomial?

A: Let's consider the polynomial x^2 + 2xy + 3y^2. To find its additive inverse, we need to change the sign of each term in the polynomial.

x^2 + 2xy + 3y^2

Changing the sign of each term, we get:

-x^2 - 2xy - 3y^2

Therefore, the additive inverse of the polynomial x^2 + 2xy + 3y^2 is -x^2 - 2xy - 3y^2.

Q: What is the significance of the additive inverse of a polynomial?

A: The additive inverse of a polynomial is significant because it allows us to simplify polynomials and perform operations such as addition and subtraction. By finding the additive inverse of a polynomial, we can cancel out terms and simplify the polynomial.

Q: Can you give an example of using the additive inverse of a polynomial to simplify a polynomial?

A: Let's consider the polynomial x^2 + 2xy + 3y^2 + x^2 + 2xy + 3y^2. To simplify this polynomial, we can use the additive inverse of the polynomial x^2 + 2xy + 3y^2.

x^2 + 2xy + 3y^2 + x^2 + 2xy + 3y^2

Using the additive inverse of the polynomial x^2 + 2xy + 3y^2, we get:

-x^2 - 2xy - 3y^2 + x^2 + 2xy + 3y^2

Simplifying the polynomial, we get:

0

Therefore, the polynomial x^2 + 2xy + 3y^2 + x^2 + 2xy + 3y^2 simplifies to 0.

Conclusion

In conclusion, the additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a polynomial with a zero constant term. By finding the additive inverse of a polynomial, we can simplify polynomials and perform operations such as addition and subtraction. We hope that this article has helped to clarify the concept of the additive inverse of a polynomial and its significance in mathematics.