To add the polynomials [tex]\(6x^2 - 5x + 3\)[/tex] and [tex]\(3x^2 + 7x - 8\)[/tex], we need to combine the coefficients of like terms. Let's break it down step-by-step:
1. Identify the like terms:
- The terms with [tex]\(x^2\)[/tex] are [tex]\(6x^2\)[/tex] and [tex]\(3x^2\)[/tex].
- The terms with [tex]\(x\)[/tex] are [tex]\(-5x\)[/tex] and [tex]\(7x\)[/tex].
- The constant terms are [tex]\(3\)[/tex] and [tex]\(-8\)[/tex].
2. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
[tex]\[
6x^2 + 3x^2 = 9x^2
\][/tex]
3. Add the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[
-5x + 7x = 2x
\][/tex]
4. Add the constant terms:
[tex]\[
3 + (-8) = -5
\][/tex]
5. Write the resulting polynomial:
[tex]\[
9x^2 + 2x - 5
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9x^2 + 2x - 5}
\][/tex]
Thus, the correct option is C.
