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Which example correctly demonstrates polynomial addition?

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8

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

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

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

1 answer

To perform polynomial addition, we combine like terms. Let's analyze the given example:

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

Now we can group and add the coefficients of similar terms:

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

Putting it all together, we have:

\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]

Therefore, the correct answer is:

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