Let's find the sum of the given polynomials step by step:
We start with the polynomials:
[tex]\[ (6x + 7 + x^2) + (2x^2 - 3) \][/tex]
First, we group the like terms together:
1. Combine [tex]\(x^2\)[/tex] terms
2. Combine [tex]\(x\)[/tex] terms
3. Combine constant terms
Step 1: Combining [tex]\(x^2\)[/tex] terms
[tex]\[ x^2 + 2x^2 = 3x^2 \][/tex]
Step 2: Combining [tex]\(x\)[/tex] terms
[tex]\[ 6x \][/tex]
Step 3: Combining constant terms
[tex]\[ 7 - 3 = 4 \][/tex]
Putting it all together, we get:
[tex]\[ 3x^2 + 6x + 4 \][/tex]
Now we compare this polynomial to the given choices:
1. [tex]\(-x^2 + 6x + 4\)[/tex]
2. [tex]\(3x^2 + 6x + 4\)[/tex]
3. [tex]\(9x + 4\)[/tex]
4. [tex]\(9x^2 + 4\)[/tex]
The polynomial we obtained is:
[tex]\[ 3x^2 + 6x + 4 \][/tex]
Comparing this with the given options, we see that it matches:
[tex]\[ 3x^2 + 6x + 4 \][/tex]
Thus, the correct choice is:
[tex]\[ 3x^2 + 6x + 4, \][/tex]
which corresponds to option 2.
