Question

Add the polynomial expressions 5z−2z2−4z+5
and 6z2+3−7z
.(1 point)
Responses

4z2−z+8
4 z squared minus z plus 8

4z2−6z+8
4 z squared minus 6 z plus 8

11z2+z−2
11 z squared plus z minus 2

9z2−11z+8
9 z squared minus 11 z plus 8

Answer 1

To add the polynomial expressions \( 5z - 2z^2 - 4z + 5 \) and \( 6z^2 + 3 - 7z \), we can begin by combining like terms.

1. **First expression:** \( 5z - 2z^2 - 4z + 5 \)
- Combine \( 5z \) and \( -4z \): \( (5z - 4z) = 1z \) or simply \( z \).
- The expression now becomes: \( -2z^2 + z + 5 \).

2. **Second expression:** \( 6z^2 + 3 - 7z \)
- This can be rewritten as: \( 6z^2 - 7z + 3 \).

Now, combine the two processed expressions:

\[
(-2z^2 + z + 5) + (6z^2 - 7z + 3)
\]

Combine like terms:

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

Putting it all together:

\[
4z^2 - 6z + 8
\]

Thus, the correct answer is:

**4z² - 6z + 8** (4 z squared minus 6 z plus 8).