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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.

Add the polynomials, then simplify:
(5x^2 + 7x + 6) + (12x^2 - 8x - 11)
(-2x^2 - 10x + 10) + (-12x^2 - 7x + 5)

Learn how to add and simplify polynomials by combining like terms. We solve two polynomial expressions step-by-step: (5x^2 + 7x + 6) + (12x^2 - 8x - 11) and (-2x^2 - 10x + 10) + (-12x^2 - 7x + 5). Suitable for students in Grades 7-9.

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