Question

Which polynomials are listed with their correct additive inverse? Check all that apply.

x2 + 3x – 2; –x2 – 3x + 2
–y7 – 10; –y7 + 10
6z5 + 6z5 – 6z4; (–6z5) + (–6z5) + 6z4
x – 1; 1 – x
(–5x2) + (–2x) + (–10); 5x2 – 2x + 10

Answer 1

A, C, D

Explanation:

we know that

If two numbers have a sum of zero, then we say they are additive inverses

so

case A)

Sum the polynomials;

They are additive inverses

case B)

Sum the polynomials;

They are not additive inverses

case C)

Sum the polynomials;

They are additive inverses

case D)

Sum the polynomials;

They are additive inverses

case E)

Sum the polynomials;

They are not additive inverses

Answer 2

x^2 + 3x – 2; x^2 – 3x + 2

6z^5 + 6z^5 – 6z^4; (–6z^5) + (–6z^5) + 6z^4

x – 1; 1 – x

Explanation:

To select the polynomial that has additive inverse, we check the sign of each term. each term has different sign then it has additive inverse

x^2 + 3x – 2

–x^2 – 3x + 2 (sign of all terms are different so correct additive inverse)

–y^7 – 10

–y^7 + 10 (sign of y^7 is same so it is not correct additive inverse)

6z^5 + 6z^5 – 6z^4

(–6z^5) + (–6z^5) + 6z^4 (sign of all terms are different so correct additive inverse)

x – 1

1 – x

-x +1 (sign of all terms are different so correct additive inverse)

(–5x2) + (–2x) + (–10)

5x2 – 2x + 10 (sign of -2x is same so it is not correct additive inverse)