Question Which example correctly demonstrates polynomial addition?(1 point) Responses (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)= 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)=5x2+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 5 x squared plus 9 x plus 10 (2x2+6x+1)+(3x2+3x+9)=−x2+3x−8

Answer 1

To correctly demonstrate polynomial addition, we need to combine like terms properly. Let's analyze the provided responses:

1. (2x² + 6x + 1) + (3x² + 3x + 9) = 13x² + 9x + 10

   • This is incorrect. The correct addition of the terms should be:
     • \(2x² + 3x² = 5x²\)
     • \(6x + 3x = 9x\)
     • \(1 + 9 = 10\)
     • Therefore, the left side should equal \(5x² + 9x + 10\).

2. (2x² + 6x + 1) + (3x² + 3x + 9) = (2x² + 3x + 1) + (3x² + 6x + 9)

   • This is also incorrect because it does not perform the addition; instead, it rearranges the terms without correctly equating them.

3. (2x² + 6x + 1) + (3x² + 3x + 9) = 5x⁴ + 9x² + 10

   • This is incorrect. The degree of polynomial terms is miscalculated. The addition should not produce a term of \(5x^4\) as there are no \(x^4\) terms in either polynomial.

4. (2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10

   • This is correct. As shown in the calculations above, the like terms were appropriately added together.

5. (2x² + 6x + 1) + (3x² + 3x + 9) = -x² + 3x - 8

   • This is incorrect. The signs and values do not match up with the expected results from the addition.

Thus, the correct response that demonstrates polynomial addition is:

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