To simplify the expression [tex]\(\left(3x^2 - 2\right) + \left(5x^2 + 5x - 1\right)\)[/tex], follow these steps:
1. Distribute and Combine the Like Terms: Combine the coefficients of [tex]\(x^2\)[/tex], the coefficients of [tex]\(x\)[/tex], and the constant terms separately.
[tex]\[
(3x^2 - 2) + (5x^2 + 5x - 1)
\][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
3x^2 + 5x^2 = 8x^2
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
0 + 5x = 5x
\][/tex]
([tex]\(3x^2 - 2\)[/tex] does not have an [tex]\(x\)[/tex] term, so we consider the coefficient of [tex]\(x\)[/tex] to be 0 here.)
4. Combine the constant terms:
[tex]\[
-2 - 1 = -3
\][/tex]
5. Write the simplified expression: Combine all the like terms together:
[tex]\[
8x^2 + 5x - 3
\][/tex]
Considering these steps, the final simplified expression is:
[tex]\[
8x^2 + 5x - 3
\][/tex]
Hence, the correct option is:
[tex]\[ \boxed{1} \][/tex]
