To find the sum of the polynomials [tex]\((x^2 + 2x + 3) + (3x^2 + x + 1)\)[/tex], we need to add the corresponding coefficients of the like terms. Let's break it down step-by-step:
1. Identify the like terms in each polynomial:
- The first polynomial is [tex]\(x^2 + 2x + 3\)[/tex].
- The coefficients for the terms are:
- [tex]\(x^2\)[/tex]: 1
- [tex]\(x\)[/tex]: 2
- constant: 3
- The second polynomial is [tex]\(3x^2 + x + 1\)[/tex].
- The coefficients for the terms are:
- [tex]\(x^2\)[/tex]: 3
- [tex]\(x\)[/tex]: 1
- constant: 1
2. Add the coefficients of the like terms:
- For [tex]\(x^2\)[/tex] terms:
[tex]\[
1x^2 + 3x^2 = 4x^2
\][/tex]
- For [tex]\(x\)[/tex] terms:
[tex]\[
2x + 1x = 3x
\][/tex]
- For the constant terms:
[tex]\[
3 + 1 = 4
\][/tex]
3. Combine the sums to get the resulting polynomial:
[tex]\[
4x^2 + 3x + 4
\][/tex]
Thus, the sum of the polynomials [tex]\((x^2 + 2x + 3) + (3x^2 + x + 1)\)[/tex] is [tex]\(\boxed{4x^2 + 3x + 4}\)[/tex].
The correct answer is:
A. [tex]\(4 x^2 + 3 x + 4\)[/tex]
