To correctly demonstrate polynomial addition, we need to combine like terms from the two given polynomials:
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \]
First, we combine the like terms:
- \(2x^2 + 3x^2 = 5x^2\)
- \(6x + 3x = 9x\)
- \(1 + 9 = 10\)
Putting it all together, we get:
\[ 5x^2 + 9x + 10 \]
Now let's check the responses:
- \((2x^2+6x+1)+(3x^2+3x+9)= 5x^4+9x^2+10\) (Incorrect, wrong degree for \(x^4\))
- \((2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10\) (Correct)
- \((2x^2+6x+1)+(3x^2+3x+9)=13x^2+9x+10\) (Incorrect, wrong coefficient for \(x^2\))
- \((2x^2+6x+1)+(3x^2+3x+9)=−x^2+3x−8\) (Incorrect, all terms wrong)
The correct demonstration is:
(2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10.
1 answer