To find the sum of the polynomials, we need to add the coefficients of corresponding powers of [tex]\(x\)[/tex]. We are given the polynomials:
[tex]\[
6x + 7 + x^2
\][/tex]
and
[tex]\[
2x^2 - 3
\][/tex]
Let's rewrite these polynomials in a standard form from the highest degree to the constant term to clearly see the coefficients:
[tex]\[
x^2 + 6x + 7
\][/tex]
and
[tex]\[
2x^2 - 3 + 0x
\][/tex]
Now we align the polynomials by their degrees:
[tex]\[
\begin{array}{r}
1x^2 + 6x + 7 \\
+ 2x^2 + 0x - 3 \\
\hline
\end{array}
\][/tex]
Next, we add the coefficients of the corresponding powers of [tex]\(x\)[/tex]:
- For [tex]\(x^2\)[/tex] : [tex]\(1 + 2 = 3\)[/tex]
- For [tex]\(x\)[/tex] : [tex]\(6 + 0 = 6\)[/tex]
- For the constant term: [tex]\(7 - 3 = 4\)[/tex]
Thus, the resulting polynomial after adding is:
[tex]\[
3x^2 + 6x + 4
\][/tex]
So, the sum of the given polynomials is:
[tex]\[
3x^2 + 6x + 4
\][/tex]
The correct answer is:
[tex]\[
3x^2 + 6x + 4
\][/tex]
