Question: Add or subtract (add the opposite): $$(4x^2 - 3x + 9) + (2x^2 - x - 7)$$
Select the correct response:
$6x^2 - 4x + 2$
$6x^2 - 2x + 16$
1. **State the problem:** We need to add the polynomials $4x^2 - 3x + 9$ and $2x^2 - x - 7$.
2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the same variable raised to the same power.
3. **Add the like terms:**
$$4x^2 + 2x^2 = 6x^2$$
$$-3x + (-x) = -3x - x = -4x$$
$$9 + (-7) = 9 - 7 = 2$$
4. **Combine all results:**
$$6x^2 - 4x + 2$$
5. **Final answer:** The sum of the polynomials is $6x^2 - 4x + 2$.
This matches the first response choice.