The problem in the image asks for adding the polynomials $(5x^2 - 9x + 6)$ and $(2x^2 + 6x - 8)$, and writing the answer in standard form.

Step-by-step solution:

1. Combine like terms:

   • $x^2$-terms: $5x^2 + 2x^2 = 7x^2$
   • $x$-terms: $-9x + 6x = -3x$
   • Constant terms: $6 - 8 = -2$

2. Write the resulting polynomial: $7x^2 - 3x - 2$

Final Answer:

$7x^2 - 3x - 2$

Let me know if you'd like further clarification or detailed steps!

Follow-up Questions:

1. How do you determine the standard form of a polynomial?
2. What are like terms, and why is it important to combine them?
3. How would subtraction of polynomials differ from addition?
4. Can this process be extended to higher-degree polynomials? How?
5. Why is it important to arrange the terms in descending powers?

Tip: Always align like terms vertically when adding or subtracting polynomials to avoid mistakes!