Ask a New Question
Menu

Which example correctly demonstrates polynomial addition?(1 point)

Responses

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative x squared plus 3 x minus 8

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to 13 x squared plus 9 x plus 10

(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to 5 x squared plus 9 x plus 10

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

1 answer

To perform polynomial addition, we need to combine like terms correctly. Let's break down the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):

  1. Combine the \(x^2\) terms: \[ 2x^2 + 3x^2 = 5x^2 \]

  2. Combine the \(x\) terms: \[ 6x + 3x = 9x \]

  3. Combine the constant terms: \[ 1 + 9 = 10 \]

Putting it all together, we have: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]

Now, let's check the response options:

  • Response 1: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) - Incorrect

  • Response 2: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\) - Incorrect

  • Response 3: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) - Correct

  • Response 4: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\) - Incorrect

Thus, the correct demonstration of polynomial addition is: Response 3: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).