Question

Add the polynomial expressions 5z−2z2−4z+5
and 6z2+3−7z
.

(1 point)
Responses

11z2+z−2
11 z squared plus z minus 2

4z2−z+8
4 z squared minus z plus 8

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

4z2−6z+8

Answer 1

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

1. Start with the first polynomial:
\[
-2z^2 + (5z - 4z) + 5 = -2z^2 + z + 5
\]

2. Now take the second polynomial:
\[
6z^2 - 7z + 3
\]

3. Now, add the two polynomials together:
\[
(-2z^2 + z + 5) + (6z^2 - 7z + 3)
\]

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

Putting it all together, we get:
\[
4z^2 - 6z + 8
\]

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