What is the additive inverse of the polynomial 9xy2+6x2y-5×3 – In the realm of polynomial operations, understanding the concept of additive inverses is crucial. This exploration delves into the intricacies of additive inverses, their identification, and their applications in polynomial manipulation.
An additive inverse, often denoted by the symbol “-,” is a unique polynomial that, when added to the original polynomial, results in a zero polynomial. In other words, it is a polynomial that “undoes” the effect of the original polynomial in an additive operation.
What is the Additive Inverse of a Polynomial?
The additive inverse of a polynomial is a polynomial that, when added to the original polynomial, results in the zero polynomial.
Definition of Additive Inverse
In the context of polynomials, the additive inverse of a polynomial f(x)is denoted as -f(x). It is a polynomial that has the same terms as f(x)but with the opposite signs.
For example, the additive inverse of the polynomial 2x2– 3x + 5 is -2x2+ 3x – 5 .
Identifying the Additive Inverse of a Polynomial, What is the additive inverse of the polynomial 9xy2+6x2y-5×3
To find the additive inverse of a polynomial, simply change the sign of each term in the polynomial.
For example, the additive inverse of the polynomial 5x3– 2x 2+ 7x – 1 is -5x3+ 2x 2– 7x + 1 .
Additive Inverse of the Given Polynomial
The given polynomial is 9xy2+ 6x 2y – 5x 3.
To find its additive inverse, we change the sign of each term:
-9xy2– 6x 2y + 5x 3
Therefore, the additive inverse of 9xy2+ 6x 2y – 5x 3is -9xy2– 6x 2y + 5x 3.
Properties of Additive Inverses
Additive inverses have the following properties:
- The additive inverse of 0 is 0.
- The additive inverse of the additive inverse of a polynomial is the original polynomial.
- The sum of a polynomial and its additive inverse is the zero polynomial.
Applications of Additive Inverses
Additive inverses are used in various mathematical operations, such as:
- Solving equations: To solve an equation of the form f(x) = a, we can add the additive inverse of f(x)to both sides to get 0 = a- f(x) , which is equivalent to f(x) = a.
- Simplifying expressions: Additive inverses can be used to simplify expressions by combining like terms with opposite signs.
Frequently Asked Questions: What Is The Additive Inverse Of The Polynomial 9xy2+6x2y-5×3
What is the additive inverse of the polynomial 2x^2- 3xy + 4y^2?
-2x^2 + 3xy – 4y^2
How can I find the additive inverse of a polynomial with multiple variables?
Change the sign of each term in the polynomial.
What are the properties of additive inverses in polynomials?
The additive inverse of a polynomial is unique. The additive inverse of the additive inverse of a polynomial is the original polynomial. The additive inverse of the sum of two polynomials is the sum of their additive inverses.
