It looks like you want to simplify the polynomial expression and choose the correct classification for it. Let's go step by step:

The given polynomial expression is: $(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2)$

Step 1: Simplifying the Expression

We start by expanding and combining like terms.

1. Distribute in the last part of the expression $(x + 3)(x + 2)$: $(x + 3)(x + 2) = x^2 + 2x + 3x + 6 = x^2 + 5x + 6$

2. Now, substitute this into the original expression: $(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x^2 + 5x + 6)$

3. Next, distribute the negative sign in the second set of parentheses: $3x^2 - x - 7 - 5x^2 + 4x + 2 + x^2 + 5x + 6$

4. Combine like terms:

   • $3x^2 - 5x^2 + x^2 = -x^2$
   • $-x + 4x + 5x = 8x$
   • $-7 + 2 + 6 = 1$

So, the simplified expression is: $-x^2 + 8x + 1$

Step 2: Answer the Questions

Now that we've simplified the polynomial expression, let's classify it:

• Degree: The highest power of $x$ is $x^2$, so the degree of the polynomial is 2.
• Type: It has 3 terms: $-x^2 + 8x + 1$, so it is a trinomial.

Conclusion

• The polynomial simplifies to a quadratic expression (because the highest power is $x^2$).
• It is a trinomial (because it has three terms).
• The degree of the polynomial is 2.

Would you like further clarification or have any other questions related to polynomials? Here are some questions you could explore next:

1. What are the different types of polynomials based on their degree?
2. How do you identify a monomial, binomial, and trinomial?
3. Can you simplify polynomials with more than three terms? How?
4. How do you factor quadratics like the one we just simplified?
5. What is the difference between a constant, linear, and quadratic polynomial?

Tip: When simplifying expressions with parentheses, always distribute terms correctly before combining like terms.