Answer :

To solve the problem of finding the sum of [tex]\(17x^3 + (3x + 8x^3)\)[/tex], we need to follow these steps:

1. Identify and Combine Like Terms:
- First, identify the terms in the expression: [tex]\(17x^3\)[/tex] and [tex]\(8x^3\)[/tex] are like terms because they both have the variable [tex]\(x\)[/tex] raised to the same power, 3. The term [tex]\(3x\)[/tex] is different because it is just [tex]\(x\)[/tex] (or [tex]\(x^1\)[/tex]).

2. Add the Like Terms:
- Combine the coefficients of the like terms [tex]\(x^3\)[/tex]:
- [tex]\(17x^3\)[/tex] plus [tex]\(8x^3\)[/tex] equals [tex]\( (17 + 8)x^3 = 25x^3 \)[/tex].

3. Include the Additional Term:
- Don't forget the separate term [tex]\(3x\)[/tex], which remains unchanged because it doesn't combine with the [tex]\(x^3\)[/tex] terms.

4. Write the Final Expression:
- After combining like terms, the expression becomes [tex]\(25x^3 + 3x\)[/tex].

Therefore, the correct answer is [tex]\(\boxed{C. \, 25x^3 + 3x}\)[/tex].

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