To find the sum of the polynomials $9x^2 - 6$ and $2x^2 - x - 10$, we simply add like terms.

Step-by-Step Solution:

1. Write the expressions with all terms aligned by powers of $x$: $(9x^2 - 6) + (2x^2 - x - 10)$

2. Combine like terms:

   • For $x^2$: $9x^2 + 2x^2 = 11x^2$
   • For $x$: There is only $-x$, so it remains $-x$.
   • For the constant terms: $-6 - 10 = -16$

3. Write the resulting polynomial: $11x^2 - x - 16$

Answer:

The sum is: $11x^2 - x - 16$

Would you like more details on how to add polynomials or have any questions?

Related Questions:

1. How do you subtract polynomials?
2. What happens when you add polynomials with different degrees?
3. How do you simplify expressions with multiple variables?
4. How can you check if your polynomial addition is correct?
5. What are real-world applications of adding and subtracting polynomials?

Tip:

When adding polynomials, align terms by their degrees to avoid mistakes in combining like terms.