The directions to a problem say "write two equivalent expressions for the opposite, or additive inverse, of each polynomial).
What is an "additive inverse"?
An example problem is:
5x³ - 7x² + 3x -6
The additive inverse, or opposite, of a polynomial refers to a polynomial that, when added to the original polynomial, results in a sum of zero. In other words, it is the polynomial that cancels out the original polynomial.
To find the additive inverse of a polynomial, you can simply change the sign of each term in the original polynomial. So, for the example problem:
Original polynomial = 5x³ - 7x² + 3x - 6
Additive inverse:
-5x³ + 7x² - 3x + 6
An "additive inverse" refers to a number that, when added to another number, gives a sum of zero. In other words, for any number a, its additive inverse is the number that, when added to a, results in zero.
In the example problem you provided, 5x³ - 7x² + 3x - 6, we need to find the additive inverse of this polynomial. To do this, we want to create an expression that, when added to the original polynomial, results in zero.
To find the additive inverse of a polynomial, we can simply change the signs of all the terms in the polynomial.
So, the first step is to change the sign of each term in the polynomial 5x³ - 7x² + 3x - 6. The terms with positive coefficients will become negative, and the terms with negative coefficients will become positive.
Therefore, the additive inverse of the polynomial 5x³ - 7x² + 3x - 6 is -5x³ + 7x² - 3x + 6.