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

Answer:

Step-by-step explanation:

a c d. simple

Answer 2

we know that

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

so

case A)

$x^{2} +3x-2$

$-x^{2} -3x+2$

Sum the polynomials

$(x^{2} +3x-2)+(-x^{2} -3x+2)=0$

therefore

they are additive inverses

case B)

$-y^{7} -10$

$-y^{7} +10$

Sum the polynomials

$(-y^{7} -10)+(-y^{7} +10)=-2y^{7}$

$-2y^{7}\neq 0$

therefore

they are not additive inverses

case C)

$6z^{5} +6z^{5}-6z^{4}$

$(-6z^{5}) +(-6z^{5})+6z^{4}$

Sum the polynomials

$(6z^{5} +6z^{5}-6z^{4})+((-6z^{5}) +(-6z^{5})+6z^{4})=0$

therefore

they are additive inverses

case D)

$x-1$

$1-x$

Sum the polynomials

$(x-1)+(1-x)=0$

therefore

they are additive inverses

case E)

$(-5x^{2})+(-2x)+(-10)$

$5x^{2}-2x+10$

Sum the polynomials

$((-5x^{2})+(-2x)+(-10))+(5x^{2}-2x+10)=-4x$

$-4x}\neq 0$

therefore

they are not additive inverses