To find the sum of the polynomials [tex]\((6x + 7 + x^2)\)[/tex] and [tex]\((2x^2 - 3)\)[/tex], we need to add the like terms together. Let's break it down step-by-step:
1. Step 1: Arrange the polynomials
Write down the polynomials in standard form, aligning like terms (terms with the same power):
[tex]\[
(6x + 7 + x^2) + (2x^2 - 3)
\][/tex]
2. Step 2: Combine like terms
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(x^2 + 2x^2 = 3x^2\)[/tex]
- Combine the [tex]\(x\)[/tex] terms: [tex]\(6x\)[/tex] (there is no other [tex]\(x\)[/tex] term in the second polynomial)
- Combine the constant terms: [tex]\(7 - 3 = 4\)[/tex]
3. Step 3: Write the resulting polynomial
After combining the like terms, we get:
[tex]\[
3x^2 + 6x + 4
\][/tex]
So, the sum of the polynomials [tex]\( (6x + 7 + x^2) \)[/tex] and [tex]\( (2x^2 - 3) \)[/tex] is:
[tex]\[
3x^2 + 6x + 4
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{3x^2 + 6x + 4}
\][/tex]
