Question

Which of the following shows that polynomials are a closed system under addition?(1 point)
Responses

(0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=3.903x2−12.84x+3.903
left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 3.903 x squared minus 12.84 x plus 3.903

(0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=1.846x2−12.84x+5.96
left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 1.846 x squared minus 12.84 x plus 5.96

(0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=2x2−13x+6
left parenthesis 0.923 x squared minus 6.42 x plus 2.98 right parenthesis plus left parenthesis 2.98 minus 6.42 x plus 0.923 x squared right parenthesis equals 2 x squared minus 13 x plus 6

(0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=10.994x2+5.96

Answer 1

To determine which option demonstrates that polynomials are a closed system under addition, we need to confirm the correct calculation for the sum of the two polynomials given.

Let's calculate the sum of the two polynomials:

1. First polynomial: \( 0.923x^2 - 6.42x + 2.98 \)
2. Second polynomial: \( 2.98 - 6.42x + 0.923x^2 \)

Now let's add them together:

- Combine the \( x^2 \) terms:
\[
0.923x^2 + 0.923x^2 = 1.846x^2
\]

- Combine the \( x \) terms:
\[
-6.42x - 6.42x = -12.84x
\]

- Combine the constant terms:
\[
2.98 + 2.98 = 5.96
\]

Thus, the sum of the two polynomials is:
\[
1.846x^2 - 12.84x + 5.96
\]

Looking at the provided responses, we see:

- The correct response that matches our calculation is:
\[
(0.923x^2−6.42x+2.98)+(2.98−6.42x+0.923x^2)=1.846x^2−12.84x+5.96
\]

Therefore, the correct response that shows that polynomials are a closed system under addition is:

**(0.923x^2−6.42x+2.98)+(2.98−6.42x+0.923x^2)=1.846x^2−12.84x+5.96**