To determine which polynomials are listed with their correct additive inverses, we need to understand what an additive inverse is. An additive inverse of a polynomial is another polynomial that, when added to the original polynomial, results in zero.
For example, if you have a polynomial like P(x) = 3x^2 + 2x + 1, its additive inverse is -P(x) = -3x^2 – 2x – 1. When you add P(x) and -P(x), you get:
P(x) + (-P(x)) = (3x^2 + 2x + 1) + (-3x^2 - 2x - 1) = 0
To check which polynomials have their correct additive inverses listed:
- For 2x + 3, the inverse is -2x – 3
- For x^2 – 4, the inverse is -x^2 + 4
- For -5x^3 + 2, the inverse is 5x^3 – 2
- For 4, the inverse is -4
The correct polynomials with their additive inverses would have to satisfy the condition above. Check all polynomials alongside their inverses accordingly.