Let's go through both problems and solve them step by step.

Question 6

We need to add and simplify the polynomials:

$(5x^2 + 7x + 6) + (12x^2 - 8x - 11)$

1. Combine the $x^2$ terms: $5x^2 + 12x^2 = 17x^2$

2. Combine the $x$ terms: $7x - 8x = -x$

3. Combine the constant terms: $6 - 11 = -5$

So, the simplified form is:

$17x^2 - x - 5$

Question 7

We need to add and simplify the polynomials:

$(-2x^2 - 10x + 10) + (-12x^2 - 7x + 5)$

1. Combine the $x^2$ terms: $-2x^2 - 12x^2 = -14x^2$

2. Combine the $x$ terms: $-10x - 7x = -17x$

3. Combine the constant terms: $10 + 5 = 15$

So, the simplified form is:

$-14x^2 - 17x + 15$

Would you like further clarification on any step? Let me know if you need details!

Here are 5 related questions to expand your understanding:

1. How do you subtract polynomials?
2. How do you handle multiplication of polynomials?
3. What is the significance of like terms in polynomial addition?
4. Can you simplify the expression $(4x^2 + 5x - 3) - (2x^2 - 7x + 6)$?
5. How do you add polynomials with more than three terms?

Tip: Always ensure that you align like terms (same powers of variables) before combining them when adding or subtracting polynomials.