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)=−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)=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)= 5x4+9x2+10

Answer 1

To correctly demonstrate polynomial addition, we need to add the like terms of the two polynomials. Let's break down the expression:

Given:

\((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\)

Now, we can add the like terms:

- The \(x^2\) terms: \(2x^2 + 3x^2 = 5x^2\)
- The \(x\) terms: \(6x + 3x = 9x\)
- The constant terms: \(1 + 9 = 10\)

Putting it all together, we get:

\(5x^2 + 9x + 10\)

Now, let's analyze the options given:

1. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \) (Incorrect)
2. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) (Incorrect)
3. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) (Correct)
4. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \) (Incorrect)

The correct option is:

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