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
15 years ago
1 year ago
The additive inverse, also known as the opposite, of a polynomial is 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 when added together.
For the given example problem, 5x³ - 7x² + 3x -6, the additive inverse can be found by changing the sign of each term in the polynomial.
First, change the sign of every term:
-(5x³) + (-(-7x²)) + (-3x) + (-(-6))
This simplifies to:
-5x³ + 7x² - 3x + 6
Thus, the additive inverse of 5x³ - 7x² + 3x - 6 is -5x³ + 7x² - 3x + 6.
11 months ago
An "additive inverse" refers to a number or an expression that, when added to another number or expression, yields a sum of zero. In other words, it is the number that, when combined with a given number, results in cancellation or nullification.
To find the additive inverse of a polynomial, you need to change the signs of all the terms in the polynomial.
Let's take the example problem you provided:
5x³ - 7x² + 3x - 6
To find the additive inverse of this polynomial, you'll flip the signs of each term.
The first term, 5x³, becomes -5x³.
The second term, -7x², becomes +7x².
The third term, 3x, becomes -3x.
The fourth term, -6, becomes +6.
Thus, the additive inverse of the polynomial 5x³ - 7x² + 3x - 6 is -5x³ + 7x² - 3x + 6.
Remember, to find the additive inverse, you simply flip the signs of each term.