Question

add the polynomial expression 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z

Answer 1

To add the polynomial expressions \( 5z - 2z^2 - 4z + 5 \) and \( 6z^2 + 3 - 7z \), we first combine like terms from both expressions.

1. **Combine like terms from the first expression:**
\[
5z - 4z - 2z^2 + 5 = (5z - 4z) + (-2z^2) + 5 = 1z - 2z^2 + 5 = -2z^2 + z + 5
\]

2. **Now write the second expression:**
\[
6z^2 - 7z + 3
\]

3. **Now add both expressions:**
\[
(-2z^2 + z + 5) + (6z^2 - 7z + 3)
\]

4. **Combine like terms:**
- **For \( z^2 \) terms:**
\[
-2z^2 + 6z^2 = 4z^2
\]
- **For \( z \) terms:**
\[
z - 7z = -6z
\]
- **For the constant terms:**
\[
5 + 3 = 8
\]

5. **Putting it all together, we have:**
\[
4z^2 - 6z + 8
\]

Therefore, the sum of the polynomial expressions is:
\[
\boxed{4z^2 - 6z + 8}
\]