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

Question

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)=10.994x2+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 10.994 x squared plus 5.96

(0.923x2−6.42x+2.98)+(2.98−6.42x+0.923x2)=2x2−13x+6

Answer 1

To determine which option shows that polynomials are a closed system under addition, we need to look for an expression where the sum of two polynomials is itself a polynomial.

The main polynomial expressions involved are:

1. \(0.923x^2 - 6.42x + 2.98\)
2. \(2.98 - 6.42x + 0.923x^2\)

Now, let's add them up:

1. The coefficient of \(x^2\): \[ 0.923 + 0.923 = 1.846 \]

2. The coefficient of \(x\): \[ -6.42 - 6.42 = -12.84 \]

3. The constant term: \[ 2.98 + 2.98 = 5.96 \]

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

Now we compare this result with the options presented:

• 1: \(3.903x^2 - 12.84x + 3.903\) (incorrect)
• 2: \(1.846x^2 - 12.84x + 5.96\) (correct)
• 3: \(10.994x^2 + 5.96\) (incorrect)
• 4: \(2x^2 - 13x + 6\) (incorrect)

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

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