Sure! Let's add the polynomials step-by-step.
We are given the polynomials:
[tex]\[ 7x^2 - 5x + 3 \][/tex]
[tex]\[ + 2x^2 + 7x - 8 \][/tex]
To add two polynomials, we add the coefficients of like terms. The like terms here are the terms with [tex]\(x^2\)[/tex], the terms with [tex]\(x\)[/tex], and the constant terms.
1. Add the coefficients of [tex]\(x^2\)[/tex]:
[tex]\[ 7 + 2 = 9 \][/tex]
So the coefficient for [tex]\(x^2\)[/tex] in the resulting polynomial is [tex]\(9\)[/tex].
2. Add the coefficients of [tex]\(x\)[/tex]:
[tex]\[ -5 + 7 = 2 \][/tex]
So the coefficient for [tex]\(x\)[/tex] in the resulting polynomial is [tex]\(2\)[/tex].
3. Add the constant terms:
[tex]\[ 3 - 8 = -5 \][/tex]
So the constant term in the resulting polynomial is [tex]\(-5\)[/tex].
Combining these results, the resulting polynomial is:
[tex]\[ 9x^2 + 2x - 5 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{C. \ 9x^2 + 2x - 5} \][/tex]
