Question

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

4z2−z+8
4 z squared minus z plus 8

11z2+z−2
11 z squared plus z minus 2

4z2−6z+8
4 z squared minus 6 z plus 8

9z2−11z+8

Answer 1

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

1. For the first polynomial \(5z - 2z^2 - 4z + 5\):
- Combine \(5z\) and \(-4z\) to get \(z\).
- The constant term is \(5\).
- Thus, this polynomial simplifies to \(-2z^2 + z + 5\).

2. For the second polynomial \(6z^2 + 3 - 7z\):
- The \(6z^2\) term stays as is.
- Combine \(-7z\) with \(0z\) to get \(-7z\).
- The constant term is \(3\).
- Thus, this polynomial is already in simplest form as \(6z^2 - 7z + 3\).

Now we can add the two simplified polynomials together:

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

Combining the like terms:

- For \(z^2\): \(-2z^2 + 6z^2 = 4z^2\)
- For \(z\): \(z - 7z = -6z\)
- For constants: \(5 + 3 = 8\)

So, the result of adding the two polynomials is:

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

Thus, the answer is **4z² - 6z + 8**.