Question

Which example correctly demonstrates polynomial addition?
Responses

(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals negative x squared plus 3 x minus 8

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10

Answer 1

To determine which example correctly demonstrates polynomial addition, let's go through each option and perform the addition.

1. **Option 1:**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x^2) + (6x + 3x) + (1 + 9)
\]
Simplifying:
\[
= 5x^2 + 9x + 10
\]

2. **Option 2:**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
This is incorrect because the addition does not produce a negative coefficient for \(x^2\).

3. **Option 3:**
This option seems to misinterpret the grouping:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = (2x^2 + 3x + 1) + (3x^2 + 6x + 9)
\]
This grouping is not valid for the addition, and also it's incorrect as per the calculation.

4. **Option 4:**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
Since we have already determined this in option 1, this is correct as well.

The correct demonstrations of polynomial addition are **Option 1 and Option 4**, both leading to:
\[
5x^2 + 9x + 10
\]