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We are asked to find \((a + b)(x)\), given the following functions:

- \(a(x) = 3x^2 - 5x + 2\)
- \(b(x) = x^2 + 8x - 10\)

### Step-by-step Solution:

To find \((a + b)(x)\), we simply add the two functions together:

\[
(a + b)(x) = a(x) + b(x)
\]

Substitute the expressions for \(a(x)\) and \(b(x)\):

\[
(a + b)(x) = (3x^2 - 5x + 2) + (x^2 + 8x - 10)
\]

Now, combine like terms:

- Combine the \(x^2\) terms: \(3x^2 + x^2 = 4x^2\)
- Combine the \(x\) terms: \(-5x + 8x = 3x\)
- Combine the constant terms: \(2 - 10 = -8\)

Thus, we have:

\[
(a + b)(x) = 4x^2 + 3x - 8
\]

### Final Answer:

\[
(a + b)(x) = 4x^2 + 3x - 8
\]

Would you like more details or explanations on any part of the solution?

Here are some related questions you might find helpful:
1. What happens when you subtract \(b(x)\) from \(a(x)\)?
2. How do you find the product \((a \cdot b)(x)\)?
3. What does the graph of \((a + b)(x)\) look like?
4. How would you factor \((a + b)(x)\) if possible?
5. How does this approach change if higher-degree polynomials are involved?

**Tip**: Always combine like terms carefully and double-check for sign errors when adding polynomials.

Find (a + b)(x) where a(x) = 3x^2 - 5x + 2 and b(x) = x^2 + 8x - 10.

Learn how to find the sum of two polynomials a(x) = 3x^2 - 5x + 2 and b(x) = x^2 + 8x - 10 by combining like terms. This problem is suitable for students in Grades 9-11 and focuses on adding polynomials step by step.

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