What Is The Additive Inverse Of The Polynomial?A. { -7y^2 + X^2y - 3xy - 7x^2$}$B. ${ 7y^2 - X^2y + 3xy + 7x^2\$} C. ${ 7y^2 + X^2y + 3xy + 7x^2\$} D. { -7y^2 - X^2y - 3xy - 7x^2$}$E. [$7y^2 + X^2y - 3xy -
In mathematics, polynomials are algebraic expressions consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a zero polynomial. In other words, it is the polynomial that, when added to the original polynomial, cancels out all the terms.
Understanding Polynomials
A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. The variables in a polynomial are often represented by letters such as x, y, or z, and the coefficients are numbers that are multiplied with the variables. For example, the expression 2x^2 + 3x - 4 is a polynomial, where 2, 3, and -4 are the coefficients, and x is the variable.
Additive Inverse of a Polynomial
The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a zero polynomial. In other words, it is the polynomial that, when added to the original polynomial, cancels out all the terms. To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.
Example: Finding the Additive Inverse of a Polynomial
Let's consider the polynomial 2x^2 + 3x - 4. To find the additive inverse of this polynomial, we need to change the sign of each term. The additive inverse of 2x^2 is -2x^2, the additive inverse of 3x is -3x, and the additive inverse of -4 is 4. Therefore, the additive inverse of the polynomial 2x^2 + 3x - 4 is -2x^2 - 3x + 4.
Finding the Additive Inverse of the Given Polynomial
Now, let's consider the given polynomial -7y^2 + x^2y - 3xy - 7x^2. To find the additive inverse of this polynomial, we need to change the sign of each term. The additive inverse of -7y^2 is 7y^2, the additive inverse of x^2y is -x^2y, the additive inverse of -3xy is 3xy, and the additive inverse of -7x^2 is 7x^2. Therefore, the additive inverse of the polynomial -7y^2 + x^2y - 3xy - 7x^2 is 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 zero polynomial. To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial. The additive inverse of the given polynomial -7y^2 + x^2y - 3xy - 7x^2 is 7y^2 - x^2y + 3xy + 7x^2.
Answer
The correct answer is B. 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 zero polynomial.
- To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.
- The additive inverse of the given polynomial -7y^2 + x^2y - 3xy - 7x^2 is 7y^2 - x^2y + 3xy + 7x^2.
Frequently Asked Questions
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 zero polynomial.
Q: How do I find the additive inverse of a polynomial?
A: To find the additive inverse of a polynomial, we need to change the sign of each term in the polynomial.
Q: What is the additive inverse of the given polynomial -7y^2 + x^2y - 3xy - 7x^2?
In this article, we will answer some of the most frequently asked questions on the additive inverse of polynomials. Whether you are a student, teacher, or just someone interested in mathematics, this article will provide you with the information you need to understand the concept of additive inverse of polynomials.
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 zero polynomial. In other words, it is the polynomial that, when added to the original polynomial, cancels out all the terms.
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. For example, if you have a polynomial 2x^2 + 3x - 4, the additive inverse would be -2x^2 - 3x + 4.
Q: What is the difference between the additive inverse and the multiplicative inverse of a polynomial?
A: The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a zero polynomial. The multiplicative inverse of a polynomial, on the other hand, is a polynomial that, when multiplied by the original polynomial, results in a constant polynomial. For example, the multiplicative inverse of the polynomial x is 1/x.
Q: Can a polynomial have more than one additive inverse?
A: No, a polynomial can only have one additive inverse. The additive inverse of a polynomial is unique and is determined by changing the sign of each term in the polynomial.
Q: How do I apply the concept of additive inverse in real-life situations?
A: The concept of additive inverse is used in many real-life situations, such as in finance, where the additive inverse of a debt is a credit, and in physics, where the additive inverse of a force is a force in the opposite direction.
Q: Can I use the concept of additive inverse to solve equations involving polynomials?
A: Yes, the concept of additive inverse can be used to solve equations involving polynomials. By adding the additive inverse of one polynomial to the other, you can simplify the equation and solve for the unknown variable.
Q: What are some common mistakes to avoid when finding the additive inverse of a polynomial?
A: Some common mistakes to avoid when finding the additive inverse of a polynomial include:
- Not changing the sign of each term in the polynomial
- Adding the additive inverse to the original polynomial instead of subtracting it
- Not considering the constant term in the polynomial
Q: How do I check if I have found the correct additive inverse of a polynomial?
A: To check if you have found the correct additive inverse of a polynomial, you can add the additive inverse to the original polynomial and simplify the expression. If the result is a zero polynomial, then you have found the correct additive inverse.
Conclusion
In conclusion, the concept of additive inverse of polynomials is an important concept in mathematics that has many real-life applications. By understanding the concept of additive inverse, you can solve equations involving polynomials and apply the concept in various situations. Remember to avoid common mistakes when finding the additive inverse of a polynomial and to check your answer by adding the additive inverse to the original polynomial.
Key Takeaways
- The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in a zero polynomial.
- To find the additive inverse of a polynomial, you need to change the sign of each term in the polynomial.
- The additive inverse of a polynomial is unique and is determined by changing the sign of each term in the polynomial.
- The concept of additive inverse can be used to solve equations involving polynomials and has many real-life applications.
Additional Resources
For more information on the concept of additive inverse of polynomials, you can refer to the following resources:
- Khan Academy: Additive Inverse of Polynomials
- Mathway: Additive Inverse of Polynomials
- Wolfram MathWorld: Additive Inverse of Polynomials