Question

Add the polynomial expressions 5 z minus 2 z squared minus 4 z plus 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. First polynomial:
\[
5z - 2z^2 - 4z + 5
\]
can be rearranged to group like terms:
\[
-2z^2 + (5z - 4z) + 5 = -2z^2 + 1z + 5
\]

2. Second polynomial:
\[
6z^2 + 3 - 7z
\]
can be rearranged to group like terms:
\[
6z^2 - 7z + 3
\]

Now, we can combine the two expressions:

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

Combining like terms:

- For the \(z^2\) terms:
\[
-2z^2 + 6z^2 = 4z^2
\]

- For the \(z\) terms:
\[
z - 7z = -6z
\]

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

Putting it all together:

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

Therefore, the sum of the two polynomial expressions is:

\[
\boxed{4z^2 - 6z + 8}
\]