Question

Add the polynomial expressions $5z-2z^{2}-4z+5$ and $6z^{2}+3-7z$
(1 point)
$9z^{2}-11z+8$
$4z^{2}-z+8$
$11z^{2}+z-2$
$4z^{2}-6z+8$

Answer 1

To add the polynomial expressions \(5z - 2z^2 - 4z + 5\) and \(6z^2 + 3 - 7z\), we first combine like terms within each expression and then add the two results together.

**Step 1: Simplify the first expression**

The first polynomial is:
\[
5z - 2z^2 - 4z + 5
\]

Combining the \(z\) terms:
\[
5z - 4z = 1z
\]

Now the expression simplifies to:
\[
-2z^2 + 1z + 5
\]

**Step 2: Simplify the second expression**

The second polynomial is:
\[
6z^2 + 3 - 7z
\]

We can arrange it for easier combining:
\[
6z^2 - 7z + 3
\]

**Step 3: Add the two expressions together**

Now, we add the simplified first polynomial \(-2z^2 + z + 5\) and the simplified second polynomial \(6z^2 - 7z + 3\):

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

Combining like terms for \(z^2\):
\[
-2z^2 + 6z^2 = 4z^2
\]

Combining like terms for \(z\):
\[
z - 7z = -6z
\]

Combining the constant terms:
\[
5 + 3 = 8
\]

**Step 4: Write the final result**

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

Thus, the answer is:
\[
\boxed{4z^2 - 6z + 8}
\]